Serverless architectures are internet based systems where the application development does not use the usual server process. Instead they rely solely on a combination of third-party services, client-side logic, and service hosted remote procedure calls (FaaS).
Serverless applications often make extensive use of third party services to accomplish tasks that are traditionally taken care of by servers. These services could be rich ecosystems of services that interoperate, such as Amazon AWS and Azure, or they could be a single service that attempt to provide turnkey set of capabilities such a Parse or Firebase. The abstraction provided by these services could be infrastructural (such as message queues, databases, edge caching…) or higher-level (federated identity, role and capability management, search…).
Read the article of serverless computing for a concise summary of what serverless is and its trade-offs. For an in-depth look at serverless architecture and as a result is a long read, refer to the link below: https://martinfowler.com/articles/serverless.html.