What it means
A very normal British way to say umbrella. It’s casual, everyday, and the sort of word you hear in homes, on school runs, at bus stops, and in weather chat every five minutes. It sounds friendly and unfussy, not posh and not especially street. If someone tells you to bring your brolly, they just mean don’t get soaked.
Usage examples
"Chuck a brolly in your tote, mate, it’s spitting again and the bus stop’s a wind tunnel. I’m not getting drenched for a ten-minute ride."
"Grab your brolly, it is chucking it down out there."
"I left my brolly on the train again, third one this year."
"You’ll want your brolly, love, that sky’s got bad ideas written all over it."
"Oi, whose brolly is this by the door? Mine’s the knackered black one that folds like a dying pigeon."
Where it comes from
Brolly is a real old British shortening of umbrella, around since the nineteenth century. The exact hop from umbrella to brolly isn't nailed down in tidy little steps, but it's long been treated as a playful clipped form in the same everyday UK lane as telly and brekkie.