No Deposit Required Bonus
These are risk-free bonuses, simply put, the casino gives you real free casino chips.

Sign Up Bonus
Almost all online casinos give you a free bonus with your first purchase at the casino. For example, a "100% sign up bonus up to $50 free" means that if you purchase $20 the casino adds $20 and you get to play with $40 , if you purchase $50 the casino adds $50 and you get to play with $100. Since the bonus is "up to $50 free", if you purchase $70 or any amount above $50 the casino still adds $50 .

Bonus T & C
Each bonus has its "Terms & Conditions". Always look for it at the casino website before playing at the casino. The two important things at the T&C are the wagering requirements and the excluded games. 
Wagering requirement is how much you have to wager before you will be permitted to cash-in. For example "Five times the sum of the purchase and the bonus must be wagered before any cash-in will be permitted." means that if the sum of the purchase and the bonus is $100 you must wager a total $500 before you can cash-in. 
At the Casino 1 credit = 1 US Dollar. For example, if you play two hands of Poker and wager 5 credits on each hand, this represents a total of 10 credits wagered. If you win one of these hands and lose the other, your credit balance will remain the same, however the total amount wagered (10 credits) counts toward fulfilling your wagering requirement.
Excluded Games are games that betting on them does not fulfill the obligations with regard to the total amount wagered.