First "I don't have a clue" question, what do different lenses do? Are they mainly for different distances and light levels?
This as well as quality and autofocus speed. Nikon and Canon also put image stabilisation in the lens not the camera. Not all lenses have it (and it's not really needed in many situations).
Your bog standard kit lens is an 18-55mm f3.5-5.6.
18-55 is the zoom range with 18 being widest (zoomed out) and 55 the most telephoto (zoomed in). This is a good basic range. If you wanted to shoot stuff a long way away you would need to either complement the kit lens with something like a 50-200 or 70-300 or replace it with an 18-200.
The f number is how wide the lens opens, the lower the number the wider the aperture. Now here's the slightly confusing bit. The kit lens is f3.5-5.6. This doesn't mean f3.5 is the widest the f5.6 is the narrowest. What is means is f3.5 is the widest aperture you can select when the zoom is at 18mm and f5.6 is the widest when the zoom is set to 55mm. Higher end lenses (like for instance the 17-50 f2.8) have a constance maximum aperture that doesn't change when you zoom.
As you widen the aperture the depth of field become smaller. This means the area in focus is shallower.
You also get what are know as prime lenses, these don't have any zoom adjustment, they're a fixed focal length. They also generally have wider maximum apertures then a zoom lens. 50mm f1.8 or 35mm f1.8 are fairly common prime lenses.
The different camera manufacturers have their own lens mounts, so a Canon lens won't fit on a Nikon camera. There are also some lens compatibility considerations especially on Nikon cameras. If you're thinking of buying a lens and camera separately I would recommending asking us if they'll work together.
There are also some other lens manufacturers, Sigma, Tamron & Tokina. They make different version of their lenses to fit different makes of camera. Quality wise these lenses are usually fine although there is the odd stinker and of course the cheaper lenses will be lower quality.