TM and HM

TM and HM are Machines that can teach Pokémon Moves.

TM
TM stands for Technical Machine. A Technical Machine in the Pokémon Universe is in the form of a CD. Pokemon Trainers can give these CDs to their Pokémon to help them to learn new moves to use against opponent Pokémon. In Pokémon Generations 1-4, TM's could only be used once, and then they disappear. Recently, though, Pokémon Black and White allowed players to use them more than once, just like an HM.

List of Technical Machines
Between each Generation of the Pokémon series, the Technical Machines featured alter their attributed numbers depending on the game, to make space for new Technical Machines introduced. A list of such are as follows:

HM
A Hidden Machine, HM for short, is in almost every way identical to a TM, except for three differences: Additionally, Pokémon on a third generation game cartridge cannot be transferred to a fourth generation game card if it knows an HM move, you must go to the Move Deleter in your game in order to transfer these Pokémon to Pokémon Diamond/Pokémon Pearl. Also when you transfer Pokémon to Black/White, through the Poketransfer, the Pokémon may not know any HMs.
 * The moves cannot be overridden by simply learning another move
 * The moves can be used outside of battle after obtaining the relevant gym badge
 * The HM can be used multiple times without breaking (this is only a difference up to generation IV; in generation V TMs can not be broken).

Trivia

 * In Pokémon Black and White, the television frequently broadcasts a program called Moves for Living, which describes move attributes and is hosted by a scientist called Dr. Technic Al. Machine. His name may be based off the term "technical machine".