One common type of hybrid surfboard design combines the high performance of a shortboard with the extra width and tail of a fish. In most cases, hybrids have some combination of extra width, thickness, length or roundness if not a little of each.
A hybrid is a good board to ride if you want a little extra something to help in less than perfect conditions but you still wish to maintain the style of a shortboard. The extra thickness can help in catching waves while extra width will help with stability. These are also good boards for surfers with a little bit more girth, but who don’t feel like only riding longboards.
Because there are so many variations of boards that can be classified as hybrids, there is no general description of how they ride. A shortboard/fish hybrid might take the vertical riding of a shortboard and give you some extra glide while taking away a bit of drop-in security. You will probably just have to ride a few different variations to get a good feel of things.