Types of Cloth Diapers


The basic premise behind all cloth diapers - you need an absorbent inner material and a waterproof outer material. The differences between types of cloth diapers exist in what form these two parts take. 
 
All-In-Ones (AIO)
All-In-One diapers are an easy and convenient diaper solution. AIOs are their own entity - the absorbent inner is connected to the waterproof outer - and are the easiest cloth diaper option on the market. At each diaper change you change the entire diaper. 
Pros: easy to put on, easy to pack in diaper bag, trim (aka close-fitting), no learning curve
Cons: can take longer to dry, more expensive (though this is changing more by the day)
All-In-Twos (AI2)
All-In-Twos are a two part diaper system. When your baby requires a diaper change, simply change the absorbent insert out of the waterproof cover, add in a new insert, and put back on your baby. These truly are the best of both worlds - easy to use yet also economic. 
Pros: easy to put on, easy to pack in diaper bag, only change the insert when dirty, trim
Cons: some hands-on work required to switch the inserts out
Pockets
Pocket diapers have an outer waterproof shell with a 'pocket' that allows you to add as many absorbent inserts as necessary to suit your little one's needs. You change the entire diaper at each diaper change. Most one-size diaper systems are pocket diapers. 
Pros: easy to put on, easy to pack in diaper bag, easy to stuff with customizable absorbency, wicking material to keep little one feeling dry, most will grow with your baby from birth to potty training
Cons: generally made of entirely synthetic fabrics, bulkier than AIOs or AI2s, must be stuffed before use, more upfront expense
Fitteds
Fitted diapers are just the 'inside,' or absorbent part of the diaper. They are cut to the shape of your baby and have elastic at the back waist and legs, thus allowing you to get a good fit with minimal amount of work. You only change the fitted, and not necessarily the cover, at each diaper change. 
Pros: more economic, trim, natural fibers, great nighttime diaper if your baby is primarily a side or front sleeper. 
Cons: requires separate cover, may require fasteners to hold in place

Contours
Contour diapers are like Fitteds in that they are just the absorbent part of the diaper and are already cut to the shape of your baby. They are different in that they do not have elastic anywhere in the diaper.
Pros: cheaper than fitteds, easy to use, natural fibers
Cons: requires separate cover, requires cover or fasteners to hold in place, because they do not have elastic there may be more poo which gets onto the cover
Prefolds
Prefolds are the 'fancy' diapers of your grandmother's generations (basically a Prefold is a 'prefolded' Flat diaper). Prefolds are a piece of cotton sewn so there is additional absorbency at the center. You then fold the Prefold into whatever shape you require, and use a cover. 
Pros: very easy to wash, incredibly economic, natural fibers
Cons: requires separate cover, multiple sizes recommended, higher learning curve, requires cover or fasteners to hold in place
Flats
Flats are the cloth diapers of your grandmother's time. A large sheet of absorbent cotton, a Flat can be folded to whatever size you need. They require a waterproof cover, and, depending on how you fold the diaper, a fastener to secure. 
Pros: total economy, no need to buy multiple sizes, natural fibers
Cons: requires separate cover, highest learning curve, requires cover or fasteners to hold in place

For more information please see Which Diaper is Right for Me?