Airlift is a toolkit for building distributed services and it is the foundation of Presto. For the most part, it's a convenience layer on top of some well-known libraries (Jackson, Jersey, Jetty, Guice, etc.), but it also has support for various things you'd typically need to build a deployable server, such as packaging, configuration, logging, instrumentation (stats), etc.
Unfortunately, we don't have any docs, so you'll just have to peruse the code. There's minimal server in the codebase to demonstrate usage of some of its features: https://github.com/airlift/airlift/tree/master/sample-server