I'll try and explain in a breif way , rather than go intot detail!
Pocket - these have an absorbent pad, or 2, that get stuffed inside a 'pocket' - so once made they go on like a disposable nappy - these are very popular for that reason as easy for dads, grannys etc - the bit that sits against the baby skin is soft and keeps the wee away from the skin.
They are quick to dry as they come apart.
Example = bum genius, blueberry
All in 1 - this is when the nappy is one peice, so it goes on just like a disposable - problem is they do take a while to dry - which is why the next type is now popular...
All in 2 - these are an outer and then absorbant inners that popper on - they are a tiny bit more fiddly but they are very quick to dry and have the advantage that if the outer is clean and dry you can popper new inserts in and reuse - saves on washing and also saves on how many full nappies you have to buy!
Example, Itti Bitti D'Lish
Flat & Wraps, these are traditional nappies where you put the terry towelling type nappy on and then add a waterproof pant on. These are really easy to wash and dry, and also good for those on a budget, and once you get the hang on how to fold them they are fine
Fitted/Shaped & Wrap - is a nappy shape that goes on and then a waterproof outer - agaian easy to wash and not tricky to use at all - but some babies who have been used to disposables for a while do not like the feeling of this kind.
Sizing
Some are called Birth to Potty BTP - this means they have poppers up the front which adjust the size, they should fit til they start potty training and can, if you find ones that work well with your baby, be a good choice financially!
Sized - as in small, medium and large - obvious! Will of course work out more expensive
Fixings
Aplix/Velcro or Poppers - personal choice really, advantage of aplix is the adjustment is much finer, but disadvantage is babies can get the nappy off easily!