When deciding on a new point and shoot camera the first thing after total size is the focal length of the zoom lens. If it is a 35mm camera try to envision 50mm as the dividing line. A 50mm lens on a 35mm camera is real close to what you eye sees. In other words, the angle of coverage of a 50mm lens will give you a picture of what you normally see without scanning your eyes side to side. If you have a lens that is a lower number than the 50mm will put more of the scene you are looking at than your eyes will normally see without having to scan side to side. That’s sort of like being able to back up from what you are trying to take a picture of without actually having to move. A lens that has a higher number than 50, will cover less of the subject. Just like moving closer to it. A zoom lens that covers 38mm to 70mm for instance gives you slightly wider angle of view than you see normally and slightly less than you normally see plus everything in between. It’s like being able to move forward to get closer or backwards to get more of the scene into your picture.
From a practical standpoint, certain focal lengths lend themselves to certain subjects. For instance, a 70mm lens is good for portraits; a 150mm lens is good for sports where you are close to the action, while a 28mm or 24mm lens works well when shooting scenery.