They're the terms and conditions that usually govern a bonus. In essence, it's the small print you should be aware of before you claim the bonus on offer. They usually specify terms such as how quickly you have to spend the bonus cash, and any deposits you have to make, in order to qualify for the bonus being offered. They're completely standard when it comes to online casino bonuses and every site will have its own unique redemption conditions that govern the terms of its welcome bonus.