What is it that men take from inside a woman's dress on the leg, on the wedding day?

It's called a garter belt, and it's a Western wedding tradition that dates back to the middle ages - one thousand years ago! The groom takes off the garter belt and tosses it to the unmarried men. The man who catches is next in line to be married (much like the bouquet toss,except for men). You won't see a garter toss quite as often these days in Western weddings though - it's not as popular as it once was.