This refers to the 2 cards that the player has. It is often hidden and only known by its owner. He can choose to reveal it or keep it private.
Note that he can choose to never know his cards before betting. It is said that he plays blind (obviously not recommended).

It's also the name we give to a round. A poker game is actually a series of hands. It is also how we quantify the volume of play a player makes. We're talking about hands per hour.