It was part of a dialogue I read some time ago:
A. "His wife is pregnant again."
B. "Really? He's got his quiver full, hasn't he?"
A. "He has, and I tell you, he should know better."
I'm inclined to believe this is BrE. Looking up "quiver" I got the following: "a case for carrying or holding arrows" Merriam-Webster
A Google search didn't help much as there is a similar quotation from the book of psalms ("Blessed is the man whose quiver is full of them. They will not be put to shame when they contend with their opponents in court.") which fills all pages.
Edited dialogue. Added one more line for clarity.
Best Answer
It is an allusion to Psalm 127:
Children are considered a blessing, and are compared to a quiver of arrows. Note, the standard versification isn't particularly helpful here - the thought really begins in verse 3.
In evangelical circles, this is a common metaphor. As a preacher, I've used it myself.
In this bit of dialogue, A is perhaps suggesting that the person they are discussing has too many kids. (This is a common pejorative against Catholics, Mormons, and some evangelicals). By stressing how full the quiver is, he is both drawing the allusion and making a joke at the same time.