Women traditionally wore it either around their waist or pinned to a belt or something at the waist and was meant to carry around all manner of useful objects to help with household tasks. It might have things like scissors, a little notebook, keys, seals, tweezers, etc. During many periods, these items were very valuable as well as useful, so it was good to keep them on one’s person so they would not be lost. During the period that chatelaines were popular, most women’s clothing didn’t have pockets and they didn’t really carry bags, so the chatelaine was a substitute.
It could also refer simply to the keys to the house. In many times and households where servants were common, much of the supplies and goods were kept locked up to prevent theft. Household silver and jewelry, obviously, but also pantries and linen closets, so having the keys to all of these was the task of the mistress of the house and the servants would have to go to her to have her unlock things so they could get supplies. Having the keys to a household was a powerful thing- and often little girls would copy their mothers by carrying “chatelaines” around that were much more like charm bracelets than any real use.
Chatelaines could be very plain or completely covered in diamonds, other jewels, and fine metals. They could also be specialized to a trade (like nursing- with thermometers, bandages, and such) or a hobby.
Of course, like everything, they could get so ridiculous that they were mocked in cartoons, like this one from a 19th century Punch magazine:
There is a book about chatelaines, apparently, if you are interested.