It's actually webserver-neutral, implemented entirely in PHP and Javascript. The basic idea is that each "pagelet" does its own data fetching and rendering and returns a thunk of HTML, js & css dependencies, onload hooks, etc, as a data structure (JSON or what have you). As each pagelet completes it is flushed down the single network connection to the client using HTTP chunked encoding.

The Javascript half of BigPipe catches those flushes, handles the dependencies, registers handlers, and slaps the HTML into place. This lays the groundwork for many things like incremental page updates, parallel execution, and so on.