Chunks are segments of the virtually infinite Minecraft maps. They are 16 blocks wide, 16 blocks long, and 128 blocks deep, which is 32,768 blocks total. Chunks are generated around players when they first enter the world. And as they wander that world, nearby chunks are generated as needed. 
The exact number of generated chunks varies in single player mode, depending on view distance and movement. In multiplayer mode, a grid with a radius of 10 (for a total of 21x21 or 441 chunks) is loaded around each player and sent to the player by default, although this radius can be configured. These chunks may have activity (mobs spawning, trees growing, water flowing, dropped items disappearing etc.), while the other world chunks are inactive, stored on your hard drive. Chunks will not save again if they were saved in the last 30 seconds. 
Slimes can only spawn in specific chunks, determined by a calculation performed on the chunk coordinates. There are a number of utilities and mods which allow the player to tell which chunks they can spawn in; see the Slime article for details. 
Creation of Chunks: Chunks are created with the help of the Map Seed, which means that the chunks are always the same if you would use the same Seed again (on the same Minecraft version at least). 
Finding Chunk Edges: Pressing the "F3" button opens the Debug screen which shows the player's X, Y, and Z coordinates. These coordinates will change as the player moves around. X and Z coordinates that are divisible by 16 represent the boundaries between chunks. EG: (96, -32) is a corner where four chunks meet. One of those chunks is between X coordinates 80 to 96 and Z coordinates -48 to -32. Another one is between X coordinates 96 to 112 and Z coordinates -32 to -16, and so on. When either X or Z crosses a multiple of 16, the player is moving across chunks. 
One can make a timer with repeaters and hook up a sticky piston to it. Put glowstone in front of the piston. The light will flicker while the piston moves and if you are up on a high pole, one can see that the light updates on the chunks at slightly different times. This can also be achieved with 2 regular pistons. 
Chunk borders are visible when viewing frozen rivers and ponds from above. (Tested in Creative 1.0.0) 
Chunk Error: A chunk error (also known as a missing chunk or world hole) is a rare error found in multiplayer mode. They are only client side, meaning that other users cannot see the chunk error unless under some very rare circumstances. Reconnecting to the server or reloading the map usually fixes chunk errors. Players can jump or fall into an errored chunk, since some players have reported falling and some have reported warping similar to arrows. Due to the way fluids are displayed, any fluids on the border of the chunk error will look as if they are flowing downwards. On non-modded servers the teleport command can be used to escape such a glitch. Items dropped on an errored chunk will fall and cannot be retrieved, however. Also, non-solid blocks can't flow into one. Blocks that are in a chunk error can reappear if you place a block in a chunk error (it gets overwritten, so the block you place gets turned into what was there) or blow it up with TNT. 
[edit] Chunk error Work-arounds Because chunk errors are usually temporary bugs where the Minecraft client was unable to load a chunk, logging out and logging back in is often all that is required to fix one. However, there are also other things a player can do to work around chunk errors. 
Players are able to walk into a chunk error, but will only glitch out.[1] They are able to ride through them in a boat or minecart - provided there are pre-existing rails. While the track will remain invisible to you, your cart will follow it. If your destination happens to be in a errored chunk, simply re-connect to the server or reload the map upon arrival to avoid falling into the errored chunk and losing your minecart.[2] 
Lighting, explosions, and other processes that update blocks within a chunk can cause chunks to re-load, making them visible. Because of this, placing torches can be used to make localized parts of chunk errors visible. 
Another type of chunk error is when a player is on a SMP server and sees a chunk that is empty. If the player walks on it, the chunk will act as if it was visible. Resending the chunks by moving away(or other means) will usually fix this. Waiting may also fix this. 
Usage of chunk errors Often, a chunk error will allow you to see a cross-section of the world, making it easy to locate ores, caves, dungeons, and other hidden structures underground. This can be exploited by marking the surface above any interesting looking veins, caverns, dungeons or other structures before re-loading the map. 
If you have a buddy on a multiplayer server with a chunk error, they are useful for guiding you from along the sides of a chunk error as they can see where you are digging. This means that your friends can point you to resources they cannot reach because of the chunk error. 
