In the most common and latest definition of serverless architectures, FaaS stands at the heart of this design.
In this type of serverless architecture, the server-side logic is written as functions, which are, primarily, invocable/triggered-over events that reside in some sort of tiny light-weight containers that may live on a per call / per request / per event basis, and are hosted and fully managed by the cloud infrastructure provider. These functions utilize other server-side resources as provided by the cloud infrastructure providers that are part of its ecosystem.
Popular examples of FaaS include AWS Lambda and Azure Functions. There could also be a single service that attempts to provide a complete set of capabilities (for example, data stores, messaging servers, and so on) around FaaS, which is inclusive of number of BaaS services. Examples of such a service provider include Parse backend or Firebase.
We have covered some more information on Azure Functions in a previous chapter of cloud architecture, so you may look that up for reference.