They are literally what the name suggests: Diapers made of cloth. Usually it's an absorbant fabric like birdseye, flannel, gauze etc. You have different types: Flat cloth diapers, which is just a big square of fabric that you fold to fit your body and pin on.
Prefolds, which you still have to fold and pin on, but which have several layers in the middle.
Contour, which are several layers of fabric sewn into a shape that is similar to what you see in disposables.
All of the above need plastic pants or some similar kind of waterproof layer on top so pee doesn't go straight through.
Then there's pocket diapers and all in ones. Pocket diapers are a waterproof shell that you either snap or stuff or lay an absorbent insert into and wash separately.
All in ones are the most like disposables, because you can just snap/velcro them on and go. They have a waterproof shell and an absorbent core made of fabric.
All cloth diapers need to be washed and dried after use, and they can last many years. Flats and prefolds can be used for many many years, plastic pants need to be replaced more regularily. All in ones are the most expensive, and the least long-lasting, but they also are the most convenient. You can mess them, but it is advised that you dispose of that in the loo. You can use a liner to make that part easier, either a disposable liner that you can flush or a fleece one, for example.
In comparison to baby diapers, adult cloth diapers need to have more layers to be adequately absorbant. I don't know how much they hold exactly, but generally a bit less than disposable ones.
I am by no means an expert, but I hope I could help somewhat^^