A welcome bonus adds money to your account, but you usually cannot withdraw it until you have wagered it a number of times. That number is the wagering requirement.
A worked example
You deposit £50 and get a £50 bonus with 35x wagering on the bonus. You must place £1,750 in bets (35 × £50) before the bonus and its winnings can be withdrawn. At an average RTP of 96%, you would expect to lose about £70 doing so: more than the bonus itself.
Tip: lower wagering (10x or less) and no maximum-win cap are worth more than a bigger headline number. T&Cs always apply.