This term should not be confused with the game mechanic known as despawning, which works in the opposite manner.
Passive mobs such as cows, chickens, and pigs spawn naturally during the day, and can only spawn on grass blocks illuminated with a light level of 9 or higher (mooshrooms spawn on mycelium blocks instead of grass blocks). Hostile mobs spawn at night, and can only spawn on blocks with a level 7 light level or lower. An area can therefore be kept free of monster-spawning by illuminating it to a light level of 8 or higher.
Most mobs can be forced to spawn in Creative Mode by using spawn eggs, although some can be spawned by building certain structures in a certain way in any mode (ex. iron golem, snow golem and the Wither).
A "spawn point" is typically the term given to the location where a player respawns after death. All players who enter a Minecraft world for the first time appear in exactly the same location in the Overworld. All features in a world are gradually generated outward in all directions from this point, as players explore their surroundings. Until a player sleeps in a bed for the first time, he/she will respawn at this initial start point each time they die. Sleeping in a bed will reset the spawn point to the bed itself. Sleeping in a different bed will reset the spawn point again to the latest bed in which a player has slept. However, if the bed a player last slept in is destroyed, they will spawn back at the original spawn point in the overworld.