Why do waiters wear black arm bands?

Answer 1

Some bartenders wear them to hold their bottle opener so that they can retrieve it quickly.

Bartenders wear armbands to hold their sleeves up so they do not get them in the drinks they are serving.

Answer 2

If it's on the forearm, it's probably to keep the hot plates from burning their skin. Long sleeved shirts offer little protection.

Answer 3

It might be so they can't pull a card out of their sleeves.