He is taking the garter off.
Traditionally brides throw their bouquet to various female guests. The guest that catches the bouquet is suppose to in theory be the next woman to get married.
Grooms are suppose to remove their bride's garter using only their mouth. After removing the garter they are suppose to throw it to male guests. Whoever catches the garter is suppose to go on a date with whoever caught the bouquet.
The dating thing never really happens, it's all in good fun.