Casino bonuses are funds that an online casino deposits into your casino account as a bonus to your deposit. Online casinos are extraordinarily competitive, so they do all that they can do to encourage players to try their casino out, including giving you extra money to do so. Casino bonuses are normally a matching amount, but some casinos have bonuses that require no deposit.
Be sure to always read the casino's terms and conditions for the bonuses they offer you. Almost all online casinos require a certain amount of action (called "wagering requirements") before letting you cash out. Some casinos also subtract the amount of your bonus from your withdrawal too. (The money is in your account to wager with, but cannot be withdrawn no matter how many times you wager it.)
Many casinos also exclude certain games from the wagering requirements for withdrawing your money. Most often they exclude blackjack and roulette, but some online casinos are so restrictive that they won't let you count anything you wager on any game besides their slots.
Another perk some casinos offer, and one that I'm particularly fond of, is ongoing match bonuses. Crazy Vegas casino is my favorite example of this. You can get up to $1500 a month in bonuses with their monthly 15% deposit bonus incentive.
Some casinos also have lists of players they call "bonus abusers", who are players that play only the minimum requirement for cashing out their bonus and then leave. Theoretically, if the casino is offering a good enough bonus, and their wagering requirements aren't too strict, someone could play at quite a few casinos in a day, taking advantage of bonus offers and playing just the minimum required to cash out, and come out profitable. This is not a good idea, because most online casinos have written into their terms and conditions that if someone is a suspected bonus abuser, they can withhold their withdrawals.
Bonuses make online gambling a little more fun, and they get you more action for your money. But they're not a realistic way to make a long term profit, because you'll eventually no longer be allowed to play at any online casinos.
There are a few casino bonus related portals. One of the most comprehensive guides to online casino bonuses is Casino Cash Journey. Another good casino bonus resource is Casino Geek's Online Casino Bonus Advice page.