Focal length is the distance at which you can get a clear focus for a picture, the hs20 for example is about 1cm - 130m I think with full zoom used. I have clear face pictures taken at 100m that when zoomed into post photo the face can be seen clearly as if 20m away so I say you can get a clear photo at 130m then zoom in and crop in photoshop etc.
The macro I am sure is at 1cm basically touching the lens when taking the shot, I am not so up on the macro abilities as that is not my kind of thing, most of my shots are wildlife ( birds etc ) apart from daily things like the kids etc
Mega pixels basically determine the clarity of an image at a certain size due to the amount of pixels per cm same as a tv, for blown up a4,a3,etc ideally you want 6+ for anything under you will be fine with any 4mp camera. You can get around the mp issue with software such as gunuine fractals which increases the mp to blow up an image while keeping original quality.
the zoom speaks for it self really, teh more zoom the further away you can be from the subject and the further away to more pixels needed which is why I favour the hs20exr as it is 16mp with 30x zoom which for birds etc is great but general stuff a few meters away etc I use 8mp as it processes faster as allows faster shooting.
Shooting in raw mode is also a bonus but only really needed if you intend on using lightroom or photoshop for some post processing as raw saves far more image data than jpeg and allows you to edit/enhance the image far more and more accurately than a jpeg image.
Think that covers the basics lol