Lots of focus points allow the camera to automatically select the area which it thinks you want the camera to focus on. In theory, this allows you to frame your shot without worrying about selecting the proper area to focus on. If you're doing people shots and you always want to focus on the closest person, this function works well if you're using live view with face recognition.
If using the viewfinder, lots of focus points means the camera has a better chance of choosing the proper area to focus on. Yes, focus points are expensive to implement when using the viewfinder, so the better cameras will have more. It's actually physical structures which form the focus points when using the viewfinder. I find that 3 focus points is no fun, 11 focus points works well, and 39+ focus points is overkill for me. However, I usually find myself using single point focus, lock my focus and then frame my shot. Having the camera automatically choose my focus point usually will end up focusing on the wrong thing, especially when shooting animals with narrow depth of field and studio shooting of industrial objects. I have my camera set up in a bizarre way where the focus control is associated with one of the special function buttons which allows me to continuously track focus or lock focus.
Another reason for having different number of focus points is product differentiation. You don't want to put all sorts of good stuff in the low-end products so it will force folks to buy the more expensive product if they want the extra features. For some, it's enough to make them buy the better product which means more money and better profit margin.
Some cameras allow you to track your subject if it moves. This, in theory, is great for tracking focus of moving critters, including children. I have found this to be a gimmick so far since I like shooting wild critters against a complicated background. Perhaps this works better in a back yard setting.
If you're getting a DSLR, try using the viewfinder for a month straight. You just may find yourself liking it better than live view. If you're not used to using a viewfinder, it will take some time to become accustomed to it. There are situations where live view is handy to use, but I find it very hard to use live view since you are fighting with ambient light on the LCD, slow update rate (makes tracking and photographing fast moving critters really hard), horribly slow focus (Sony is the exception), really bad battery life (important to me since I like to go out in the bushes for a couple weeks where there's no power or go on holiday and not bring a charger), hard to frame images, difficult to do manual focus, hard to track fast moving subjects due to bad holding ergonomics, and hard to hold the camera steady at arms length. There are more evils regarding live view, but I think I've beaten the subject to death.
On manual focus, since digital SLR focus screens are unsuitable for manual focus, most people use the auto focus functionality and may even use single point focus like I do. In the old days, we had split and micro prism focus screens which worked great for manual focus. BTW, you'll be hard pressed to find a pro using live view. Pros need to operate efficiently which live view is not. The only time I use live view for stills is if I need critical focus which is usually studio shooting of inanimate objects. Live view uses contrast focusing which is very precise and horribly slow, especially shooting action shots. Phase focusing, which the viewfinder uses, is much faster, but is not as precise in certain cases.
See http://graphics.stanford.edu/courses/cs178/applets/autofocusPD.html for a nice demonstration on phase focus. You'll need to wait for the demonstration applet to load which will show you how phase focus works.