No it doesn't mean peer-to-peer here. It means that there is no one server but a lot and in fact the 'server' is abstracted away from the developer so he sees no server (serverless).
I think Wikipedia has a nice explanation of the term:
Serverless computing is a cloud-computing execution model in which the cloud provider dynamically manages the allocation of machine resources. Pricing is based on the actual amount of resources consumed by an application, rather than on pre-purchased units of capacity.[1] It is a form of utility computing.
Serverless computing still requires servers, hence it's a misnomer.[1] The name "serverless computing" is used because the server management and capacity planning decisions are completely hidden from the developer or operator. Serverless code can be used in conjunction with code deployed in traditional styles, such as microservices. Alternatively, applications can be written to be purely serverless and use no provisioned servers at all.
I don't know man, when we say "defenseless", we mean it has no defense. "Useless", it has no use. We don't mean "it has so many uses that you can't really pick one". That would be "useful", I guess, which is pretty much the opposite.
It means that the price cannot be meaningfully quantified en masse, the price is set at the moment of purchase.
Art is a good example of this as it generally has no immediate utility, and even it cultural significance is created less by the piece itself, but rather by it's philosophical foundation which is not part of the purchase (nor even ownable).
The Mona Lisa may be 'priceless', but all the money in the world is just a lot of money.
People effectively map “server” to mean “centralization botteneck” or “Single Point Of Failure” these days. In both of those senses, this system is “serverless.”
Why do we need to keep inventing new terms, though? We have perfectly apt terms already, "decentralized" and "distributed", with much more exact meanings.
Well, "distributed, decentralized, peer-to-peer network" worked well enough, back when, to differentiate e.g. Kademlia from Napster.
But interestingly, people also called BitTorrent a "distributed, decentralized, peer-to-peer network", even though BitTorrent requires trackers. None of those adjectives allow the differentiation of the Kademlia design (a network of dumb nodes with smart, active clients that walk them) from the BitTorrent design (a network containing both dumb client nodes and smart server nodes, where the clients register with the servers.)
"Serverless" is the word for what Kademlia is and (pre-DHT) BitTorrent isn't. Or what differentiates a wireless mesh routing system from a 1980s BBS store-and-forward architecture. Or what differentiates IPFS from, say, the network consisting of all Lotus Notes clients + all Lotus Domino servers.
(The funny thing is that AWS Lambda is not "serverless" by this definition. AWS Lambda is just a PaaS with a CGI-alike ABI. Now, if Lambda was an ABI standard; and everyone ran a mesh of their own Lambda nodes; and your newly deployed Lambda function could end up running on any random node, without a first-class "server"/second-class "client" node separation; then that'd be "serverless." It'd also basically be Ethereum or Urbit or another of those wacky architectures, rather than Lambda any more.)
It's used now as official term on AWS and probably other clouds as well. Its the new hot thing since you don't need to provision any servers or infrastructure. All you do is write code and deploy it to a cloud platform. And it's much much cheaper as well.
So yeah it's a dumb term but it's here to stay. :)
Cheaper? I have no idea what running a particular app would cost. The ridiculously fine grained way in which the big IaaS providers charge for their services is a major reason why I'm avoiding them whenever I can. It's just too risky, too complex and too brittle. Any tiny change can have huge cost implications.
From what I've read if you had a single instance of a lambda function running 24/7 it's still cheaper than the micro EC2 instance. You have warm-up time on initial requests if the functions been idle for awhile, but otherwise the response time is fairly quick <25ms and it scales up with your traffic directly. It's cheap for a web application served primarily from CDN with serverless for backend logic and easy entry to using other AWS services with secure access per function. Starting a web app through serverless would be insanely cheap barrier to entry with serverless considering you only pay for processing time.
Whether this works well depends largely on the architecture of the application and if it's done right. You can absolutely have a serverless application that would be much better served with elastic beanstalk or ECS perhaps but to say serverless is useless or too expensive all around is not true.