This figure of speech
means the greater part in any allotment, especially that share given to the leader.
The phrase originates from one of two Aesop's fables, The Lion, the Fox, and the Ass (which can be read in that writeup) or another fable, which may have been severely distorted from the former over time, and is generally regarded as less reputable than the other one. It isn't significantly different in meaning, but substantially it's more tedious and complicated, as shown by the title: The Four Hunters, the Lion, the Heifer, the Goat, and the Sheep. Hence, I won't include it here.