Just like Kung Fu in the 70's, serverless application development and deployment is hot. But just like Kung Fu, serverless is as much of a mindset as it is a platform. Amazon's Lambdas really kicked off the excitement, but going even further back, the origins of this style of programming can be found in functional principles: those found in Erlang, Haskell, and Scala.
Primarily, the idea of stateless computing and the goal of building discrete application functions drive this new paradigm of serverless. What's new about serverless is the fact that applications are offered up to the cloud to run in some unknown nebula managed by the cloud provider, with scaling needs completely abstracted away from the developer.
That's the promise, anyway. For the older readers out there, this probably sounds a bit like an elaborate new form of application server. And you'd be completely right. To this end, both IBM and Oracle's approach to the serverless revolution has been to offer open source runtimes for anyone to run in their own cloud.