Structure

Every specific group of blocks purposefully formed in Minecraft based on coding is part of a natural structure.

The Overworld
The Overworld contains numerous generated structures, at a wide variety of scales.

Terrain
Biomes dictate the shape and height of the world. At this stage, the ground is made mostly of stone and stone variants, with water filling in most empty spaces below layer 63, with exception for structures.

Mountain
Mountains are hills with extreme slopes and cliffs. Mountains can sometimes have caves through them. On an amplified world, mountains are extremely common in all biomes except ocean and swamp biomes.

Floating "island"
Floating "islands" are structures that float in midair that are not connected to the ground, the sea, hills or cliffs. Floating "islands" are normally just random pieces of floating dirt and stone found near cliffs, but on rare occasions they can be large, floating structures that even have springs and trees on them. Floating Islands are most frequently found in mountains biomes (and its variants), along with the "hills", "mountains", and "modified" variants of most biomes, especially shattered savannas.

Hollows
Hollows are the opposite of floating islands. They look like caves, but they have nothing to do with cave generation (although they may intersect with them). When there are many overhangs, they close together and create a hollow. They have exactly the same floor as the terrain above, depending on the biome that they are located in, unlike caves. Hollows have no specific floor. Grass blocks can generate inside too, and interestingly will survive without light. When they generate under the sea level, they are filled with water. They are extremely rare in the default world, but can be found far more commonly in certain customized worlds.

Hill
Hills are randomly generated pieces of land in the map. Like stairs, hills are always traversable to their lowest point by virtue of the algorithm which generates them; there is almost always a place on each level from where the next level can be accessed, meaning that the player can climb a hill one level at a time until they reach the top. Cases where this is not true are rare.

Surface layer
The uppermost layers of the terrain are converted to a biome-dependent material: usually grass blocks and dirt, or sand in deserts and beaches. Podzol is found in giant tree taiga, mycelium in mushroom field biomes, and red sand is found in the badlands biome. Sandstone is generated under sand.

Basin
Occasionally, instead of being converted to dirt or sand, the top layer is stripped away, leaving a 'basin' of bare stone. They bear some resemblance to a geological 'shield' (an area of tectonically stable rock that has been exposed to prolonged erosion due to its very old age; it is distinct from the geological term "basin"). They seem to be more common in forest or plains, and are occasionally seen filled with water. Commonly, minerals can be found in these, generally coal ore and iron ore. If generated in a Badlands biome, gold ore can also be seen.

Lake
Lakes are shallow and often small bodies of liquid. Water lakes, which are small pools of water springs, can generate above sea level or inside caverns. They can also generate isolated underground, connected to no other structures whatsoever. When in a winter biome, these small lakes are never initially frozen but will turn to ice if exposed. The lakes can also be composed of lava; however, lakes of lava are much rarer. Lava lakes found at the surface are surrounded by stone (which can be replaced by ore veins such as dirt, gravel and coal). Both types of lake generate with a small air pocket above them, which may result in floating sand, floating snow cover or even the top two-thirds of trees above the lake. Lava lakes may cause trees to burn away.

Ravine
Ravines are tall, thin trenches that generate either underground or at the surface, and extend 30 - 50 blocks downwards or to bedrock level in the Bedrock Edition. Ravines can spawn in the ocean making it look like underwater trenches.

Small structures
The quantity of most of these features (aside from dungeons, mineral veins, and springs) is biome-dependent; not all features can be found in every biome.

Mineral vein
A mineral vein is a natural deposit of ores. Players can come across these veins in caverns or anywhere where there is natural stone. Underground deposits of dirt and gravel are generated in this step, followed by the more precious ores: coal, iron, gold, redstone, diamond, emerald (in mountains biomes) and lapis lazuli. They can only form in stone, and do not replace each other or any other block. However, there is one exception: other ores can replace andesite, diorite and granite. Note that two or more mineral veins can form next to each other and make it look like a mineral vein made of more than one material.

Spring
Springs are randomly generated blocks of either lava or water that act as a source of their respective material. While both can be found on the vertical side of stone blocks above the surface, lava springs are more often found underground beneath layer 32 in caverns and mineshafts. They do not generate above a certain Y altitude.

Mossy cobblestone boulder
These structures are meant to represent boulders, made entirely of mossy cobblestone. The arrangement of these structures varies greatly. They can be found dotted around areas of the giant tree taiga biome. Mossy cobblestone boulders are quite rare, due to the giant tree taiga biome's rarity.

Ice spike
Ice spikes are tall spires made of packed ice that can only be found in the snowy tundra biomes. There are two variants of ice spikes: one is short and thick, and the other is extremely tall and thin.

Iceberg
Icebergs are structures that generate in frozen oceans and their deep variants. They consist primarily of packed ice with a little bit of ice and blue ice, and will often be topped with snow. They are the only place where blue ice can be found naturally. Icebergs generate in a wide variety of shapes and sizes, ranging from small "islands" to giant mountain-like ice structures. They can also generate with "cave-like" holes in them, which sometimes reach to the other side of the iceberg. Polar bears and strays can also spawn here, much like other cold biomes.

Buildings
Buildings are naturally generating structures that form above ground. They can contain valuable treasure, but traps and puzzles as well.

The Nether
The Nether, though equally vast, contains far fewer types of generated structures than the Overworld.

Lava sea
Lava seas are found at and below level 30 in the Nether. They make a large portion of the Nether, and are extremely common. They can stretch for hundreds of meters in any direction, and are usually bordered by netherrack (or more rarely soul sand and/or magma blocks).

Glowstone clusters
Glowstone clusters are typically veins of glowstone that can be among the hardest natural materials to harvest that don't require digging. They form in coral-like structures on the underside of hanging Netherrack, so they are often found on the ceilings of the Nether, where they provide light along with the ever present lava.

Other things located in the Nether
There are areas of soul sand and gravel around layer 64, veins of nether quartz ore, large "veins" of magma blocks and "hidden lava", which is a single block of lava generated randomly between netherrack.

The End
The End is the final and most barren dimension, with very few types of significant structures, until after defeating the Ender Dragon, which will open gateways to more structures.

The Central Island
The center of the End is a large, asteroid-like island composed entirely of end stone, floating in the void. At a distance of 1000 blocks away, an endless expanse of more islands begins, away from the main island. These consist of large islands, about the size of the main island, and smaller ones, which are usually very thin and small.

Obsidian platform
The obsidian platform is a 5 by 5 square of obsidian that is generated once a player enters the End. (Note that if the obsidian is destroyed, or if a block is placed on top of it, when the player enters the End, the obsidian will be restored and any blocks on top of it will despawn.) Obsidian platforms generate at X, Y, Z = 100(100.5), 48, 0(0.5), mostly far away from the island, making it tough to get there. Players who enter the end will spawn at X, Y, Z = 100, 49, 0 and the other entities that enter the end will spawn at X, Y, Z = 100.5, 50, 0.5, the middle of platform and 1 block higher than the platform.


 * Sometimes the platform generates inside a case of end stone. It will remove enough end stone so that the player can walk around.
 * Occasionally the platform will generate in midair.

Chorus tree
Chorus trees generate on the outer islands of the end. They are formed in tall, coral-like patterns.They consist of chorus stems and chorus flowers. A chorus flower will generate at the top of each branch. They are the only source of chorus fruit and chorus flowers. The player can grow a new chorus tree by planting a flower on a block of endstone.

Return gateway
Return gateways are end gateways that generate randomly throughout the outer End islands. These will teleport the player back to the center island's spawn platform.

Technical details
Structures are generated for a given chunk after the terrain has been formed. The chunk format includes a tag called TerrainPopulated that indicates whether structures whose point of origin is in that chunk have been generated. If it is false or missing, they will be generated again. Structure generation is based on what is already in the chunk, so (for example) flagging a chunk that has already been populated for repopulation will approximately double the amount of ore in it.

When structures are generated, they can spill over into neighboring chunks that have been previously generated. Thus, a tree at the edge of the generated world (and probably only visible using external tools) may be overwritten by a lake before the player reaches it. It is also theoretically possible for two worlds generated with the same seed, from the same version of Minecraft, to differ slightly depending on the players' travel routes, because the order in which chunks are generated may determine which of two conflicting structures will overwrite or suppress the other.

Videos
Some of these are outdated.

Trivia

 * In previous versions, before snow cover was solid, a lava lake with floating snow cover above it could be a deadly trap before the snow melted.
 * The smallest possible fully-grown chorus tree (assuming the growth is not obstructed) would have 5 chorus plants.