to have one's fill: to eat or have enough of something until the appetite or need is met
At its root this word is about reaching the point where a hunger is met and there is no longer any lack. Most often that hunger is literal: a person eats and is full, livestock graze and are full, the land drinks rain and has had enough. The word names the moment of completion, not the eating or drinking itself.
From there the same idea stretches in two directions without changing its core. When God is the one who satisfies, the word turns positive and generous: he fills the hungry with good things, satisfies the poor with bread, fills a long life with days. When a person reaches past enough into too much, the same word turns sour: to be glutted, fed up, sick of a thing, sated to the point of loathing it.
The word can also leave food behind entirely and describe being satisfied in the deepest sense, content because the one true need has been met. The clearest cases are the ones where a person is satisfied not with bread but with God himself, with his favor, his presence, his likeness. The English picture of being full holds all of this together: the question is always what fills you, and whether enough has tipped over into too much.