Definition of button
The button is the chip on the poker table that says "DEALER". This is the button that identifies who the dealer is in the hand. In the casino, this term is symbolic since usually (unless you are in a friendly game), it is not that player who will be playing the dealer role, but a designated dealer who is not playing. When we talk about the button, we are talking about the player who has the button and is therefore the dealer (the player in position).
Additional details on the button
In each hand, the button will move clockwise. If a player was button on one hand, the next hand the button will move to the left and the next player will have that role. The button is important because it determines the player in position (the player to talk last on all streets after the flop). The button also determines the blinds. The player to the left of the button will be the small blind and the player to the left of the small blind will be the big blind. When we talk about the button, we are not usually talking about the button that says "DEALER", but about the player in position, the dealer. In short, the button is a position on a poker table just like the small or big blind.