There’s more than one way the maxim is used, but generally it is used to refer to contradictory or contrast opposites–you know, things that you cannot usually have both at the same time.

For instance, someone gives a lot of time to his work/her work but still has a happy home life.

Or someone is given a lot of money but arranges it so he/she can take time to sail a boat or camp out often.

Or someone gets a job as a travel writer, for whatever reason, and is paid to go to interesting places, but spend the rest of the time in a nice house where he/she enjoys being.

So “The best of both worlds” refers to having two things a person usually can’t have at without forfeiting one of them.

Origin:

BEST OF ALL POSSIBLE WORLDS, THE – “The optimal condition, quite often as it is seen by an optimist like Dr. Pangloss in Voltaire’s ‘Candide’ (1759): “in this best of all possible worlds.all is for the best.’