Meaning: It is better to have things that are certainly yours , than taking a risk to obtain some more.
Important point: A risk should be involved i.e. the person should be in a position where he loses what he has when he goes for "some more"
So one should not say " You got 10 out of 25 marks in exam. Live with it, do not work for more. A bird in the hand is worth two in the bush" . This statement would be wrong, because urge for marks in exam doesn't really have any risk involved. This similarly also applies for a minister who wants to work more for the public etc.
"You are investing all your money in a company you can't trust. Weren't you good with the previous business? Remember a bird in the hand is worth two in the bush" Here the person is risking all his money into an untrusted company in spite of having a good-going business of his own, just for earning "some more"