It's "no servers" for the developer in the sense that there is zero infrastructure to manage, configure or deploy. This is popularly known as a "PaaS" or platform as a service, ala Heroku and similar providers.
You're not paying for a server being up for you 24/7, you're not managing a server, you don't worry about what's being provisioned. That's what "no server" means, yes everybody knows there's a server! There's no magic hat tricks! It's just a new trend word now :), say "no server"
What you say makes no sense. There is a server , you just don't manage it yourself.
> it's a function on the backend
And where is the "backend" ? that's right , on a server.
> It's being called by the JS SDK on the browser,
What does the SDK call ? a server when your functions lie.
Lambda + api gateway are a BAAS. You might have some logic running in the browser but the lambda functions run @AWS. So there is a server.
It's a bit like Couch Apps by the way,except that you can scale at the 'design document level', not just at the 'node level'.