A glitch (also known as a bug) is a mistake or error that players may encounter during gameplay, due to their fault, or randomly.
In Minecraft, a glitch can range from missing textures, to items missing from chests upon loading a world, to duplicating rails with pistons. Glitches are an inevitable side-effect of game development, which are always present when the game is updated. Updates add new features or change how the game functions, which can have unintended side-effects that affect other game mechanics. Staff at Mojang constantly work on fixing these bugs while producing updates, as sometimes a glitch can make the game aggravating, or even unplayable.
Because of the vast amount of bugs and glitches that have historically occurred throughout the life of Minecraft, it's difficult to list every single one of them on this wiki. However, Mojang tracks known bugs and glitches that are in Minecraft, and lists them in a bug tracker which can be found here.