The root cause of kickback is the workpiece getting pinched between the blade and the fence. There are a couple of reasons why this happens:
The most common reason is that the workpiece turns slightly (i.e. doesn't stay tight against the fence) while pushing it through. Keep in mind that the teeth on the blade are slightly wider than the rest of the "meat" of the blade. This means that during an ideal cut, the only parts of the blade ever to contact the workpiece are the teeth. In reality, however, if you're not careful to constantly push the workpiece up against the fence, it can turn a little, and the front corner can come into contact with the inner part of the blade. The friction between the blade and the workpiece causes a force which wants to further turn the workpiece which causes the workpiece to bind even harder, causing more friction which causes even more turning and binding until, a fraction of a second later, the piece comes flying back at you at mach 10. Inevitably, despite rotating rapidly through the air, it will strike you in the gut with its sharpest point every time.
This scenario happens almost exclusively when you are cutting something which is wider than it is long. It's also the reason why you should never use the miter gauge at the same time as the fence, unless you're VERY careful to apply pressure to keep the piece between the blade and the fence pushed tightly against the fence or against the miter gauge. This also happens fairly frequently when cutting very large pieces of plywood. Despite your best efforts to keep the piece held tightly against the fence, it's way too easy to torque the workpiece and bind it against the blade. On large sheets of plywood, once it binds on the blade, it usually rides up on top of the blade where it gets hurled at you at high velocity, leaving a nice rustic scarring pattern (and possibly some blood stains) across the face of the plywood.
Note that in opposition to Brian's advice, ripping a 1" strip off a 24" piece is LESS likely to cause binding (and, hence, kickback) by keeping only 1" between the blade and the fence. The larger the ratio of length:width of the piece between the blade and the fence, the better.
Another common reason for kickback is improper use of a pushstick. If you're ripping a piece 2" or wider, you can pretty safely push the piece through with your fingers. When the piece is narrower than that, however, you'll want to use a pushstick or scrap of wood to push it through without getting your fingers too close to the blade. If you don't use a pushstick and simply guide the piece along from outside the blade, the part between the blade and the fence will most likely be shot backwards once you finish the cut. This is a lot less violent than the other scenario, however. Depending on it's length, the piece usually only flies 5 or 10 feet.
Kickback can also occur when cutting warped boards. Sometimes even straight boards will warp once you cut them and release the tension from the grain. This warping can sometimes cause the piece to push away from the fence and bind into the blade. In most cases where warping is an issue, you'll be talking about ripping boards that are at least a couple of feet long. That usually means that the length:width ratio is high, so you're not that likely to experience kickback. You may, however, experience enough binding to burn the wood or even bring the blade to a screeching halt. This can be a dangerous situation, as you don't want to remove you hands from the workpiece allowing the blade to start back up and throw it backwards, but you also need to shut the power off as soon as possible. Often, the circuit breaker on the motor or in your breaker panel will trip in this case. A splitter can help immensely to avoid this problem.
You can also experience kickback (and rough looking cuts) when the blade isn't perfectly parallel to the fence. You'll want to make sure your saw is adjusted to keep the blade, fence, and miter slot all parallel to each other.
Last, if you try to cut pieces that are exremely small, especially without a zero clearance insert, you're almost guaranteed that the piece will kick back at you. The good news it that the pieces are light enough not to break any ribs when they hit you. The bad news is that such pieces are sometimes small enough to penetrate the skin rather than just bruise. They also tend to ricochet in random directions adding to the fun and sport.