Real Dictionary

armband
Armbands are plastic rings filled with air that people who are learning to swim wear on their upper arms to help them float.
countable noun: An armband is a band of fabric that you wear round your upper arm in order to show that you have an official position or belong to a particular group. Some people also wear a black armband to show that a friend or relation has died.

armband in American English
a cloth band worn around the upper arm, as in mourning or as a symbol of rank, membership, etc.
noun: a fabric band worn around the upper arm as a badge or symbol

armband in British English
noun: a band of material worn round the arm, such as one bearing an identifying mark, etc, or a black one indicating mourning