Server push works by sending js, css, images etc. just after responding to a request, instead of waiting for the client to receive the html, parse it and request the resources, saving a round trip. But pushing js, css, images, fonts etc. for example.com/about when those same files already got downloaded by the client when it fetched example.com a minute ago is a complete waste of bandwidth, because the client already has those files.
Keeping state server-side for each request seems expensive, and that's cannot be how it's done, since HTTP is stateless. Presumably, the client would re-request the html on subsequent visits, to see if anything's changed.
How does the HTTP2-server know what files to push?
There are several techniques for that. The browser can for example reset the streams. Or cache digests can be used.
Here is more information on that:
https://www.shimmercat.com/blog/cache-digests/
Just today some people are having an interesting conversation on cache digests:
https://lists.w3.org/Archives/Public/ietf-http-wg/2016AprJun/0371.html