The hen stops laying for the entire time she is broody, and for some weeks after that. It varies a bit from one hen to another.
If you "break" a broody hen (cause her to quit being broody), she may start laying eggs again in less than a week (if she just went broody), or she may still take a month or more.
A laying hen has a whole clump of egg yolks inside her body. One is full-sized and will be in tomorrow's egg. The next one is a little bit smaller, but will be full size in time for the next day's egg. The next one is a little smaller yet... down to the pinpoint-sized ones that haven't started to get big yet.
When a hen goes broody, her body starts absorbing those egg yolks. This helps keep her from starving to death while she sits on the next. She will come off the nest to eat sometimes, but not usually enough to really keep her going. So she absorbs the egg yolks and also uses up some body fat she has stored.
If a hen uses up all those egg yolks, it will take her several weeks to grow new ones up to the correct size before she can start laying again. But if you break her broodiness quickly, she has not used up the yolks yet, so she does not have as much preparation to do before she can start laying again.
How to break a broody hen is another topic. People have various favorite ways. My own favorite: move her to a safe place where you want her to hatch eggs.

Some hens will happily sit on eggs in the new place, but some are determined to only sit in the place they chose. So if I shut them in the new place, they pace back and forth trying to get out, and a few days of that is very effective at breaking their broodiness. I've decided it is easier to move the hen and see what happens, rather than deciding what I want and trying to get the hen to go along with my plan.