- You must buy the game in order to play infdev.
Infdev is a mode still under development, available only to those who have bought the game. Its main feature is generating maps of incredible size (8 times larger than the surface of the Earth, according to Notch). Currently, it generates strange landforms, including floating islands and strange looking cliffs that do not form normally in Indev. If you die, you can respawn at your starting point, but you drop all the items you were carrying (you can pick them up again if you can reach your body before the items expire). This makes it a good idea to build a base directly over your spawn point, making sure not to obstruct it.
It is possible(although not reccomended) to literally mine out of the map, showing that it is not actually infinite in a physical sense. You will indeed fall for infinity if you succeed in breaking out, but you will also lose that save as there is no way to get out of the fall and you will just be stuck there for eternity. To do this, you must mine til you hit bedrock. Work around the bedrock as this is the final layer of the map to break into the skybox.
Mobs and more realistic trees have been added on April 15th, 2010, although, at the time of writing, the trees were rolled back in order to improve performance.
Infinite map replacement
Sometime before alpha mode is finished, all game modes will be replaced with versions that create infinite maps. However, it has been confirmed that while Infdev will replace Indev as the main focus of Minecraft post-beta, smaller maps will still be available for those with less powerful computers or who just like the "less to worry about" atmosphere of current Indev style maps. (reference)