This is an extremely idiomatic English expression which is very difficult to understand without prior knowledge and understanding. It does not, as one may imagine, refer specifically to nature, birds or bushes.
The expression is used to mean that it is better to have an advantage which is certain than to have a larger advantage which is uncertain and therefore may end in nothing. The proverb attests to the idea that a person should be happy with what they have rather than always aspiring to have more and more which can ultimately end in disaster.
The proverb dates back to Medieval times and relates to the fact that at the time a bird in the hand (aka the falcon) was extremely valuable and therefore was worth more than two in the bush (aka the prey).
The first recorded use of this proverb can be dated to 1670 in John Ray’s A Hand-book of Proverbs which reads “A [also ‘one’] bird in the hand is worth two in the bush.”
Prior to this use there had been similar expressions which were used to have the same meaning such as “a living dog is better than a dead lion,” and “a byrd in hand – is worth ten flye at large.” However, nowadays these are never used and have been replaced by “a bird in the hand is worth two in the bush.”
An example of this proverb in use can be found in a quote by the American writer, George Ade who stated “a bird in the hand may be worth two in the bush, but remember also that a bird in the hand is a positive embarrassment to one not in the poultry business.”