Nest boxes ARE more for our convenience than for the chickens, who really don't care where they lay. That is, they pick odd spots, which aren't odd to them. Nest boxes make it easy for us to go only to one place to gather eggs, and they also protect the eggs from foot traffic (and possible breakage). Keeps the eggs cleaner, usually. Hens do prefer privacy for a laying location, and that's what nest boxes are meant to provide, a little room in in which to lay eggs. Safely.
The trick most folks - including me - use is to put golf balls in the nest. They look sorta like eggs, and hens tend to lay where other hens have found safe places to lay. "Oh, that looks like a good spot, there's another egg already there!"
Going broody is what happens when a laying hen experiences a hormonal change and is driven to set on a clutch of eggs to hatch them. You can't make a hen go broody, it either happens or it doesn't. When they are broody, they sit on the nest - with or without eggs under them! - and flatten their bodies out to cover the nest and the eggs in the nest. They puff their feathers up to look bigger and badder and will make growling noises, maybe even peck at anybody close to them, warning them away from the family they're trying to produce. They do not leave the nest except for one, maybe two times a day, to poop a REALLY BIG AND SMELLY POOP, drink some water and eat some food. They don't roost, they stay on that nest 24/7. They also get a sort of glazed look in their eyes, like they're in a trance. The Broody Trance. They do not expend much energy while they are brooding, so they can survive without much food during this time.
Some folks, before they learn much about chickens, think every hen will lay on her eggs and hatch them. This is not true. The majority of hens lay their eggs and leave them, day after day. For their entire lives. Some breeds are more known to have hens go broody than others, but there are always exceptions.
I always recommend folks visit (and bookmark) this link, which is very informative about chicken breeds:
http://www.ithaca.edu/staff/jhenderson/chooks/chooks.html