I never understood the term. 99% of computing is a client talking to some sort of server. Forgoing a server leaves just the client (which I think is what 'serverless' implies)
It doesn't mean there is no 'server' component. It's supposed to mean that the devs don't have to worry about the underlying server infrastructure that is running their code. They simply specify the code and the conditions under which it gets executed, and the serverless service takes care of running it.