'Broody' is when they sit on the nest for most of the day(except to get up to eat/drink/poop/dust) and all night for 3 days running.
Eggs in a hidden nest won't start to develop until a hen starts sitting on them for a few days.
She knows how long she can leave them to eat/drink/poop/dust....the warmer the weather the longer she can be off the nest.
Whether those eggs would hatch depends on several factors:
Are they fertile(do you have a rooster), is she big enough to cover 16 eggs, can she sit there with predator being a probem for 21 days?
Other birds might lay there too during the 21 day incubation, these should be removed daily.
Lots to learn about incubation with broodies, but first:
You'll need to decide if you want her to hatch out some chicks, and how you will 'manage' it.
Do you have, or can you get, some fertile eggs?
Do you have the space needed? She may need to be separated by wire from the rest of the flock.
Do you have a plan on what to do with the inevitable males? Rehome, butcher, keep in separate 'bachelor pad'?
If you decide to let her hatch out some fertile eggs, this is a great thread for reference and to ask questions.
It a long one but just start reading the first few pages, then browse thru some more at random.
https://www.backyardchickens.com/t/496101/broody-hen-thread
If you don't want her to hatch out chicks, best to break her broodiness promptly.
My experience went like this: After her setting for 3 days and nights in the nest, I put her in a wire dog crate with smaller wire on the bottom but no bedding, set up on a couple of 4x4's right in the coop and I would feed her some crumble a couple times a day.
I let her out a couple times a day(you don't have to) and she would go out into the run, drop a huge turd, race around running, take a vigorous dust bath then head back to the nest... at which point I put her back in the crate. Each time her outings would lengthen a bit, eating, drinking and scratching more and on the 3rd afternoon she stayed out of the nest and went to roost that evening...event over, back to normal tho she didn't lay for another week or two.
Water nipple bottle added after pic was taken.
Might also want to think about training your free range birds to lay in the coop again:
Free range birds sometimes need to be 'trained'(or re-trained) to lay in the coop nests, especially new layers. Leaving them locked in the coop for 3-4 days (or longer) can help 'home' them to lay in the coop nests. Fake eggs/golf balls in the nests can help 'show' them were to lay. They can be confined to coop 24/7 for a few days to a week, or confine them at least until mid to late afternoon. You help them create a new habit and they will usually stick with it. ..at least for a good while, then repeat as necessary.
