A turnover requirement (sometimes called rollover, playthrough, or wagering requirement) is the amount of times a bonus needs to be wagered before it becomes withdrawable cash in your account.
Let's say you claim a bonus of $500 and the turnover on that bonus is 1x the bonus amount. In this scenario you would have to wager a total amount of $500 and win your bonus bets in order to convert your bonus credits or bonus bets into cash.
You can learn more about how bonuses work and what to look out for here.