The best way to make data appear to move faster over the Web is to move less of it and lossless compression has always been a core tenet of good web design.
Sometimes that is done via over the top gzip of text resources (html, js, css), but other times it is accomplished via the compression inherent in the file format of media elements. Modern sites apply gzip to all of their text as a best practice.
Time marches on, and it turns out we can often do a better job than the venerable gzip. Until recently, new formats struggled with matching the decoding rates of gzip, but lately a new contender named brotli has shown impressive results. It has been able to improve on gzip anywhere from 20% to 40% in terms of compression ratios while keeping up on the decoding rate. Have a look at the author's recent comparative results.
The deployed WOFF2 font file format already uses brotli internally.
If all goes well in testing, Firefox 44 (ETA January 2016) will negotiate brotli as a content-encoding for https resources. The negotiation will be done in the usual way via the Accept-Encoding request header and the token "br". Servers that wish to encode a response with brotli can do so by adding "br" to the Content-Encoding response header. Firefox won't decode brotli outside of https - so make sure to use the HTTP content negotiation framework instead of doing user agent sniffing.
[edit note - around Oct 6 2015 the token was changed to br from brotli. The token brotli was only ever deployed on nightly builds of firefox 44.]
We expect Chrome will deploy something compatible in the near future.
The brotli format is defined by this document working its way through the IETF process. We will work with the authors to make sure the IANA registry for content codings is updated to reference it.
You can get tools to create brotli compressed content here and there is a windows executable I can't vouch for linked here