If a hunter has shot one bird, he should be satisfied with that and not go off looking for the ones that flew away. We use the proverb to mean that it is better to accept something small than to reject it and hope to get more later on.
‘The antique dealer said I might get ten pounds for the vase if I took it up to London, but he himself wasn’t prepared to give me more than a fiver for it. A bird in the hand, I thought, and accepted his offer.’