Flat nappy means any nappy that is not shaped and needs a cover to be waterproof e.g. prefolds and terry squares. Often perceived as difficult to use and old fashioned, terries remain popular among those looking for reliability at a great price. The learning curve may be steeper at the beginning but once you know, you know! Prefolds in particular are also popular with those using hybrid nappy systems, as a cheap and reliable alternative to a more expensive pad-folded insert.
If you are looking at flat nappies to use as part of a hybrid system, you might also like to look at the Inserts & Boosters reviews.