A "convincing performance" means that someone has done something, like acting or playing a sport, in a way that makes other people believe they are really good at it. Full definition
He had a very convincing performance in the first half. (justarsenal.com)
«I think when you do something for real you get a much more convincing performance from the actors,» he said. (businessinsider.com)
Nevertheless, there are undoubtedly still big question marks over their display and they'll need to produce more convincing performances moving forward. (caughtoffside.com)