Garter belts were invented before "elasticized" panty hose and "garters" were even worn by men to hold up socks and were worn below the knee on the shins. both have little clips on the front and back that attached to the hosiery to hold them up. There are also elasticized garters which were strips sewn with the ends together that were slid up to the thigh over the top of hose on each leg.The strip style "garters" were also worn on long sleeves by men who needed to keep the sleeves from trailing in their worl Below is a pic of a men's garter.. (would show the others but I don't want to offend anyone with "racy" photos) https://encrypted-tbn1.gstatic.com/shopping?q=tbn:ANd9GcRIiPdQldkwJE3cHnRR-VZLjVJl3NYm9wy3zuLUT7y2scjWEvd8OPNCK8ID_QE&usqp=CAE
I think your talking about the garter that is around the thigh of a women at her wedding? A long time ago people would sneak into their room and take it as proof that they are now married and it was suppose to bring them good luck. Now they throw it at weddings also for good luck and it's said the person that catches it will be married next.