A brolly is just an umbrella. That is the whole meaning. The extra information is who says it: it is British, chatty, a bit cosy — the kind of word a weather presenter or a grandmother might use. Americans do not say brolly; they say umbrella. In Taiwan you can leave it on the page as a British flavour-word: if a London story says “Don’t forget your brolly”, they mean an umbrella, nothing fancier. It is informal. You would not write it in a serious report. You might well hear it in a shop in England: “brollies are over there”.

雨傘（英國口語）