You will come accross 2 sets of numbers usually, the first will be the focal length measured in mm. This might be 18-55mm, 70-300mm, 10-20mm anything really. You can also get fixed focal lengths like 35mm, 50mm, 100mm.
The Focal length is simply the view the lens gives you.The smaller the number, the more view you get into a photo, the bigger the number, the more zoomed in you get, so a smaller view.
The next numbers will be the aperture. This is the hole in the lens that lets the light in.
This is usually written like this
1:3.5-5.6
Looks complicated, but it isnt. Ignore the 1:
The next is 3.5. This means the lens at its widest setting (so 18mm on a 18-55mm lens) the aperture can only go as low as f/3.5. As you zoom the lens in further, the aperture (the hole) narrows.
Once you hit 55mm, the widest the aperture can go is f/5.6.
Of course at any time you can go higher than those numbers, so in most cases up to f/22, but not lower.
More expensive lenses have fixed apertures. This will be displayed as 1:1.8 or 1:2.8
This simply means throughout the focal length, the aperture can always be f/1.8 or f/2.8. Again you can always go higher.