The term re-buy usually refers to poker tournaments where players are allowed to buy more chips immediately after losing their stack without having to leave their table.
For example, in a $100 tournament with $100 re-buys, if you lose an all-in, you can immediately ask for a re-buy. You’ll receive a full stack of chips and pay $100 on the spot without having to go to a cashier or move to a different seat.
It is different from re-entry tournaments, where you need to leave the table after you lose all of your chips and will be seated in a different spot if you buy in again.
Apart from tournaments, the expression is also used in cash games, where you can re-buy after you lose your stack. Unlike tournaments, re-buying at cash game tables offers more flexibility, as you can buy back into the game for different amounts, anywhere from the table minimum to the maximum buy-in allowed.