Bonus wagering is the number of times you must play through a bonus (and sometimes a deposit too) before it converts into money you can withdraw.
For example, if you deposit £10 and the wagering requirement is x50, you will need to wager £500 before you can cash out.
With that said, no deposit bonuses wagering works differently. Because no deposit has been made, winnings from free spins are credited as a bonus that must be then wagered. Therefore, if you win £20 and the wagering requirement is x50, you will now need to wager £1,000 before you can cash out.