WebKit is a browser engine used by many browsers, such as Safari and Web, and also by numerous other applications.
In the early days of WebRTC there were activities to add WebRTC support to WebKit (by Ericsson Research, Google, Nokia, Samsung and others.) However, this work was not followed through and, combined with the many changes to the WebRTC specification since then, a lot of changes are needed.
The good news is that an effort to fix this, using OpenWebRTC, has been launched at webrtcinwebkit.org.
You're welcome to join us there and help to make WebRTC in WebKit happen!