What it means
Means to complain loudly, kick off, and generally make a bit of a scene, usually because you’re annoyed or trying to get something sorted your way. It can be justified, like when a service is proper rubbish, or it can be over the tiniest thing. Either way, everyone nearby is going to hear about it.
Usage examples
"He kicked up a fuss in Tesco because the self-checkout ate his tenner, and the manager refunded him plus a meal deal. Absolute scenes."
"She kicked up a fuss at the airport when they tried to charge for a bag that clearly fit the rules."
"No need to kick up a fuss over the seating, we can just shuffle round when the others arrive."
"The bloke at the pub kicked up a fuss because his chips turned up cold, carrying on like they'd ruined Christmas."
"Mum kicked up a fuss with the school after they lost Jake's lunch box for the third time, and fair enough really."
Where it comes from
This one’s been around in English for ages. It comes from the older sense of fuss meaning noisy agitation or pointless flapping, with kick up used for causing or stirring something up. So if you kick up a fuss, you’re not just annoyed, you’re actively making the noise and drama bloom in the room.