What it means
Natty means smart, neat, and properly well dressed. If someone looks natty, they’ve clearly put some care into it and it shows. Crisp shirt, polished shoes, hair behaving itself. It’s a warm old-school compliment with a slightly posh little shine to it, closer to dapper than flashy or fashion-forward.
Usage examples
"Turned up to the pub in a crisp suit and shiny brogues, and everyone went, blimey, you’re looking natty tonight, mate."
"Granddad turned up to the wedding looking proper natty, three-piece suit and shoes you could see your face in."
"That's a natty wee jacket, where did you get it, it goes perfect with the boots."
"You’ve scrubbed up proper for date night, mate. That coat’s dead natty."
"Saw him at the races in a little tweed number and thought, fair play, that’s a natty look."
Where it comes from
Natty has been around in English since at least the 18th century, used for someone neat, trim, and smart in their appearance. It stuck in British English as a compliment for tidy stylish dressing, with a faintly old-fashioned, polished feel that still hangs on now.