A bug is usually a fault in the code resulting in unintended features/functions. They are usually fixed in updates. Some bugs are actually kept in and made as a feature. (Like the secret trapdoors) Note, a bug is not the same as a glitch. A glitch is a bug that is really really funny as hell. (Like the swing set in GTA 4)
See Also
- Report bugs here. (Bitbucket)
- Minecraft Wiki page of bugs.