"Serverless" really means "your code is run as a container with a finite lifetime on an arbitrary machine in a standardized, non-configurable PaaS machine cluster."
In essence, it's a return to the "cgi-bin" model of scripting, where you write a script that only runs for the lifetime of one request, and then a web server will spin it up to respond to a relevant request and it'll terminate at the end of that request.
The only differences in the modern instantiation of the concept, are that:
1. the "cgi-bin" directory is a mounted object store, common to an entire cluster; and
2. there's some fancy preloading logic that lets Lambda functions stay "hot" between calls to them, so that they can run very quickly. (Sort of like Phusion Passenger does for Ruby code, except with enough isolation to make it safe for multitenant environments. Heroku's old Alpine stack might be a better comparison.)
