What differentiates WebRender from the renderers of all other modern browsers is that renderers have traditionally operated in "immediate mode", where the renderer itself draws items on the screen one at a time, whereas WebRender operates in "retained mode", where the renderer declaratively shunts all the heavy work to the GPU. (And note that I'm hardly a graphics programmer at all, so I may have butchered this.)
Some relevant links:
pcwalton's great demonstration of the initial WebRender prototype from February (page demos start at 26 minutes): https://air.mozilla.org/bay-area-rust-meetup-february-2016/
WebRender 2 overview: https://github.com/servo/servo/wiki/Webrender-Overview#webre...
A short walkthrough of WebRender 2: http://www.masonchang.com/blog/2016/7/18/a-short-walkthrough...
I believe a long-term goal is to get WebRender into Firefox itself, but this would be quite an invasive surgery (and AFAIK wouldn't be able to 100% obviate Gecko's current renderer, for legacy reasons(?)) and so shouldn't be expected in the near future (though Stylo, another large Servo component, should hopefully be landing in Firefox this year).
EDIT: Oh, and of course, Servo is a new browser engine from Mozilla and written in Rust (though it wouldn't be entirely inaccurate to also say that Rust was written for Servo, at least originally :P ).