Just about the same thing as a Renaissance Festival, only the time period is a little earlier. At a medfair, it is fashionable to go around looking like a Celt, Scot, Gaul, Moor, generic dark ages person, or anything else that isn't the lace-and-frills of typical Renaissance dress. After all, the Renaissance is for sissies, real men wear armor!
A fun thing to do at a medfair if you're female - go in costume, but not in a dress - wear lots of weapons, and lots of leather helps too. It doesn't even have to be racy psuedo-lingerie-type leather. Even if you're covered neck-to-boots like I was, you will still get oogled like you've never been oogled before. The guys will give you this pained look that's a cross between "geez, she looks like she could kick my ass" and "damn, she's hot!"