The buy-in is – as its name suggests – the amount of money required to be able to take part in (buy in to) a game.
In a tournament setting there could be a buy-in of, for example, $10+1 which consists of $10 which goes towards the total prize pool, plus an additional $1, which is the online poker operator’s fee for hosting the tournament as part of their overall product/service. A so-called Rebuy tournament allows for multiple buy-ins during a specific period.
For Cash games the buy-in refers to how much needs to be paid in order to join a game. There are usually both minimum and maximum buy-in levels. For example, a $50 Max Cash game might have $15 minimum and $50 maximum buy-ins.