Concave is a curved bottom surface.
Usually concave is not across the whole bottom, but takes a ⅔ of it, so basically there is no concave on the tips and next to the edges. Exactly this height difference provides high pressure from the mid to the tips and edges, pushes the board up and makes a better planning rather than just a flat bottom..
Of course this characteristic is more for a kiteboard, but sometimes you may see it on a wakeboard with a flat bottom (on the ones that are without canals and redans obviously).
Has the same mechanics as a solo one but has a couple of advantages: due to an angle between a board and water, some parts of a solo concave are not completely profitable, but in a double one a part beneath water works way better. Besides, soft landings are a great addition because one part of the bottom becomes some kind of a keel and ‘divides’ water smoothly (not that good as a ships’ keels, but still…) There are other variations of complex concaves, but they all work the same way.
Concave is a very useful thing in a kiteboard because it affects the board planing and a good matching with rocker provides the best comfort to your ride.
Boards with double or complex concaves are more preferable because it directly affects riding characteristics: not only planing, but the better stability and softer landings.