Normally in a poker tournament, when your chips are out so are you. However, some tournaments allow players to buy more chips one or several times during a defined time period at the start of the tournament, much like in a regular cash game.
Buy-in, re-buy, and add-on
For apparent reasons, this kind of tournament is called a re-buy tournament. The time period during which you may re-buy is called the re-buy period.
Mostly, the right to re-buy is coupled with some kind of condition regarding your chip count. Either your stack must be below a certain value, for example, the number of chips you started out with, or you must be out of chips completely. The cost of a re-buy is often identical to the original tournament buy-in, and the number of chips received when re-buying is often identical to the number of starting chips, but these things may vary.
At the end of the re-buy period, players may be given the right to buy an add-on, that is, yet a number of chips at a certain, pre-defined cost. The add-on usually is not connected to any chip count requirements, but is open to all remaining players.