There are basically 4 different systems of nappying - all-in one systems, like Tots Bots Easyfits, Pocket nappies, like Bumgenius, Popin nappies like Close Parent - these all come with waterproofing built into the system - and a 2 part system, where you have a separate nappy and wrap - either square nappies, prefolds or shaped nappies.
The 2 part system is the most efficient, as any leaks from the nappy get caught by the wrap, and also the most economical to use, as you only need a few wraps.
The wraps waterproof the nappy. You can get nappies made out of cotton, bamboo, hemp micro-terry or tencel (which is like bamboo, but made out of wood pulp, and doesn't shrink)
PUL wraps are the most widely used, and are very good. However, fleece and wool ones are much more breathable, allow evaporation to take place, and are therefore much cooler. Lanolized wool is the Rolls Royce of fabrics to choose for nappy covers, as wool is naturally anti-bacterial, will not absorb smells, and doesn't need washing every time, but only needs hanging to air between uses, unless it has actually been soiled. I know that sounds bizarre, but it's really true you will only need to wash wool nappy cover every 3-4 weeks, unless it has been soiled! It is also very soft against the skin, so you won't get parks around the legs and waist.
Fleece has almost the same cooling properties, but will still need washing after every use, as it doesn't have the self cleaning properties of lanolized wool