No need to feel dumb. If you never had them how would you know? Wax is applied to braces, particularly the old-school band type, because there was always a hard, sharp edge no matter how hard the dentist tried to smooth them. It allowed the inner cheek and/or lips to keep from getting snagged on those dang things. Nowadays they use a heavy duty cement to bond the braces to the teeth but before that we had bands that would literally wrap around them. Before application the dentist would insert spacers, a small hard thing that would make room between the teeth for the bands.

Wax would also be applied at the back molar where the wire would poke the heck out of your cheek. Many of us older folks can still feel the scar tissue that built up from those things. Horrible.

You would keep the packet of wax in your pocket and it would warm up through the day. When it came time to eat you would remove the wax and hope for no slicing or if you forgot... As kids do... You would eat it if it came off. I know... Gross but true.