The second number in a tyre size refers to the width of the tyre in inches.
It is not an exact measurement, one manufacturers 2.0 may be as wide as anothers 2.2 but in general you can get slicks down to 1.5 for MTB wheels, XC tyres are normally 1.9-2.1 and downhill and freeride tyres start at about 2.3 and go up to 3.0!
A narrower tyre is lighter and will normally have less rolling resistance but will have to be run at higher pressure and won't have as much grip.
The width of your rim doesn't have anything to do with your choice, choose based on your riding style and be aware that even a small difference like 2.1 to 2.3 can make a huge difference!