Cloud-chasing is just shorthand vaper speak for producing massive clouds of vapour when you vape. This might sound a lot like sub-ohm vaping, which is a more common technique that also results in bigger vapour production, but cloud-chasing takes it to the extremes.
It’s also called stunt vaping because of the degree of skill and technical knowledge required as well as the performance aspect (vapers compete to blow the most interesting clouds, as well as the largest, such as rings, streams or shapes like ‘the jellyfish’).