HTTP/2 provides a mechanism for a server to push both requests and responses to connected clients. Up to this point we've used that as a browser cache seeding mechanism. That's pretty neat, it gives you the performance benefits of inlining with better cache granularity and, more importantly, improved priority handling and it does it all transparently.
However, as part of gecko 36 we added a new gecko (i.e. internal firefox and add-on) API called nsIHttpPushListener that allows direct consumption of pushes without waiting for a cache hit. This opens up programming models other than browsing.
A single HTTP/2 stream, likely formed as a long lasting transaction from an XHR, can receive multiple pushed events correlated to it without having to form individual hanging polls for each event. Each event is both a HTTP request and HTTP response and is as arbitrarily expressive as those things can be.
It seems likely any implementation of a new Web based push notification protocol would be built around HTTP/2 pushes and this interface would provide the basis for subscribing and consuming those events.
nsIHttpPushListener is only implemented for HTTP/2. Spdy has a compatible feature set, but we've begun transitioning to the open standard and will likely not evolve the feature set of spdy any futher at this point.
There is no webidl dom access to the feature set yet, that is something that should be standardized across browsers before being made available.