On tires the first number 700c, 26" etc is the wheel size that the tires fit on - it refers to the diameter of the inside of the wheel. The second number x21 x28 x32... is the width of the tire. Most rims can accept tires of more than one width, though there are limitations and you won't find any one rim that can take all sizes.

If you want wide tires with tread you can look for cyclocross tires which come in 700c sizes. Some manufactures make tires specifically for hybrid bikes too and offer some variety as well. Don't expect to walk into any bike shop and see 100's of different tires hanging up though. Ask and you'll probably be shown a catalog.