Means suspicious, dodgy, or straight-up dishonest behaviour. You’ll hear it a lot as no funny business, basically a warning to behave and not try anything sneaky. The joke is that there’s nothing funny about it, it’s the kind of “fun” that ends with a disciplinary, a bollocking, or the police having a nosey.
"There’s funny business with the till again. I swear I put a tenner in and it vanished faster than Dave at his round. No funny business today, yeah?"