It's better to have a little of something which you own than there to be a lot of something which you don't own and can't get to. Don't know about the origin though.
I think it originates from the days of hunting with falcons. A 'bird in the hand' - is a bird on its owner's wrist, which can be released when suitable prey appears. This has to be better than two birds 'in the bush' - or flying free, and out of sight in the ground bushes, and therefore beyond its handler's control.
As to the origin, it is at least as old as the Greek writer, Plutarch, who wrote in the first century AD: "He is a fool who lets slip a bird in the hand for a bird in the bush."
I was under the misconception that the adage was "A bird in the bush was worth two in the hand," which I never really understood :) Now I get it - it's better to have something than to want something that you can't see, because you never know what you might get (see Proust).