There are two primary kinds of blur in photos (well, three, but we’ll assume you keep your camera fairly clean): focus blur and motion blur. Here are examples of focus and motion blur, respectively (click to enlarge):
Focus blur happens when the subject of your photo is simply out of focus. The solution to that is to make sure your autofocus is on and try again. If it’s out of focus, re-focus and shoot again. Pretty straightforward. On point and shoot cameras, the most likely reason you’re out of focus is because the subject moved or the smart focusing system wasn’t so smart and focused on the wrong object.
Motion blur, on the other hand, doesn’t happen because your subject is out of focus. It happens because your subject is moving relative to the camera frame while the exposure is being made AND the shutter speed isn’t fast enough to freeze it. Let’s tackle those two aspects separately.