A bird in hand is in our possession. We are sure of it. But we are not sure of catching birds in the bush. They may fly away when we try to catch them. We thus lose the one in hand and fail to catch those in the bush. The saying thus means that we should not let go our sure gain and run after uncertain gains, though their value may be greater. The story goes that a wolf had caught a share. He was going to kill it for his food. At that time he saw a deer. It was a bigger animal. The wolf left the hare and ran at the deer. But he failed to catch the deer. He came back and found that the hare had gone away. He lost both.
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The proverb holds well in human life also. A man is sure of one thing. It is within his reach. He is not satisfied with it. He wants more and better things. He gives up the sure thing. He tries for a better thing but fails. He loses both. A wise man should not do this. He should make the best use of the sure thing instead of running after uncertain things, though they may be better. A man waits for a bus to go to a place quickly. A tram passes by. He does not get into it. The bus comes very late. He fails to reach the place in time and suffers loss.