What it means
Means a bunch of people are furious about something and they’re making it everyone’s problem: complaining, writing letters, signing petitions, turning up to meetings, the lot. It started off literal, as in people taking up weapons and being ready to fight. Nowadays it’s usually figurative, but it still suggests serious, organised outrage rather than a quiet moan.
Usage examples
"The whole village is up in arms about the new road, so the council hall’s rammed and everyone’s waving leaflets like it’s the end of days."
"The whole street was up in arms about the new parking charges, petitions taped to every other lamppost."
"Fans were up in arms over the kit redesign, as if the badge had personally insulted their families."
"Parents are up in arms about the school cutting breakfast club, and the local Facebook group’s turned into a full-blown war zone."
"Everyone went up in arms when the landlord binned off the heating again, so now there’s a group chat, a complaint letter, and three neighbours threatening the papers."
Where it comes from
This goes back to the literal idea of being armed and ready to fight. In English it's been around for centuries, first about actual rebellion or combat. Over time it shifted into figurative use, but it still keeps that charged image of people getting stirred up together and ready for a proper public battle.