These serverless architectures handle everything for running your app for you, and they go a mile further than application platforms like Heroku. You upload your code, which is only a collection of functions written in JavaScript/Java/Python. These functions have a single purpose: reply to HTTP requests. They can communicate with other services (AWS or not; e.g. databases) and do any kind of processing. Amazon gives you a HTTP endpoint and lets you build REST-like APIs that call these methods. When you get a call, AWS will run your function on one of their servers. Your code only runs when a request comes in, and if there are a lot of them, it just runs on multiple servers. You are billed for the time your functions run and the memory they use. Amazon does everything for you: scaling, cross-datacenter availability, networking, security.
The idea sounds groundbreaking (literally nothing to manage except application code), but in practice I have found Lambda + API Gateway (the product for piping HTTP requests to Lambda functions) both very hard to use, with a very poor UX. Also, one of the downsides of having to load functions before execution is that response times are bad (500ms+). However, if you have enough traffic, you may get reasonable performance when your service has "warmed up", thanks to caching.
I'll take a look at hook.io, but here's their product page: https://aws.amazon.com/lambda/details/ (I'd suggest you look at the pricing page too)
Lambda is more like CGI-in-the-cloud than applications in a VM.
If you are looking for portability, you could use docker. If you are looking for abstraction, you could use almost any high level language.
What is the benefit of doing it this way?