I never understood why these platforms, which clearly run on a server, were marketed as "serverless". They seem more akin to a distributed operating system, to me
Of course ultimately the code runs on a server, but it's not a server that the customer has to buy, rent, maintain, or otherwise think about.
For us this is by far the biggest factor. Innovation tokens are the most expensive thing there is.
Basically it's "serverless" because you the developer are not doing anything with servers. You're not writing one, maintaining one, or managing the infrastructure to run one. You drop off a blob of logic to the cloud provider and they handle everything else for you, and you pay on demand.
Functions-as-a-Service (FaaS) is another name for the same idea but less catchy
CGI-Bin
Mainframes
which were deeply out of fashion at the time.