This means (Adorable Representative M.C for Youth) In Hangul (아미)
They are the fanbase of The Biggest Boyband BTS (Bangtan Sonyeondan/ 방탄소년단)
They are the biggest fanbase in the world and most inspired fanbase. They are really passionate when it comes to BTS. If they need to vote, stream, buy they will make it for them. They make anything for BTS. This is also the fandom that once you talk something bad about their fave/idol they will defend their fandom but if you did something really wrong the most scary things that they can do to you is to track your location and know some of your personal information.
They ain't called ARMY for nothing ;)

Some Special Nickname of ARMYs in each country:
Korean ARMYs - Diamonds/K-Diamonds
International ARMYs - I-Lovelies
Philippine ARMYs - Pearls/PH Pearls
Japanese ARMYs - Jems
Malaysian ARMYs - Myracle
Indonesian ARMYs - Indomy
Chinese ARMYs - Cuties
Singaporean ARMYs - Sapphire
Thailand ARMYs - Treasures
ang many more...