The meaning
> A smaller advantage which can be taken now is better than a greater one at some uncertain time in the future. In essence, don’t be greedy and stick with what good things you already have, instead of going after something you’ll probably never get.
If I were you I would accept the money they’re offering. After all, a bird in the hand…
You can also find the following expression: a bird in your hand is better than 100 in the wood.
Etymology
> This idiom can be traced back to medieval days. It refers to medieval falconry where a bird in the hand (the falcon) was a valuable asset and certainly worth more than two in the bush (the prey). The first citation of the expression in print in its currently used form is found in John Ray’s «A Hand-book of Proverbs», 1670.
However, a much older Near Eastern origin is suggested by a near equivalent in the 6th century BC Proverbs of Ahiqar: «a sparrow in thy hand is better than a thousand sparrows flying».
Wrong translation
> Un oiseau dans ta main est préférable que deux dans le buisson
Correct French idiom
> Un “tiens” vaut mieux que deux “tu l’auras”