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 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.
https://en.wikipedia.org/wiki/Serverless_computing