Like many other marketing buzzwords, the concept of "serverless" has taken on a life of its own, which can make it difficult to understand what serverless actually means. What it really means is that the cloud provider fully manages server infrastructure all the way up to the application layer. For example, GCE isn't serverless because, while Google manages the physical server infrastructure, we still have to deal with patching operating systems, managing load balancers, configuring firewall rules, and so on. Serverless means we merely worry about our application code and business logic and nothing else. This concept extends beyond pure compute though, including things like databases, message queues, stream processing, machine learning, and other types of systems.
There are several benefits to the serverless model. First, it allows us to focus on building products, not managing infrastructure. These operations-related tasks, while important, are not generally things that differentiate a business. It's just work that has to be done to support the rest of the business. With cloud —and serverless in particular — many of these tasks are becoming commoditized, freeing us up to focus on things that matter to the business.