The expression hand history refers primarily to online poker, and it stands for an electronic record of all the actions in a particular hand. Hand histories are usually automatically generated by poker sites, but there are also tools that allow you to create these manually.
A proper hand history contains all the relevant information about the hand, including the number of players at the tables, blind/ante details, pot size, and all actions (bets, raises, etc.) from the very first action before the flop until the last action or the showdown.
Because they contain all these details, hand histories are a very important resource for players looking to get better. They can help you recognize certain patterns in your and your opponents’ play, fix some leaks, and discover areas of the game that you need to work on.