Quantum is a current Mozilla project encompassing several software development efforts to improve the Gecko web browser engine of Firefox.
The goal is to replace both the CSS and GPU rendering components of Gecko with those of Servo, while also making other changes to Gecko. Mozilla hopes to complete this work by the end of 2017.
Background
Gecko is a mature, full-featured engine that originated at Netscape in 1997. It's a large codebase written in the C++ language.
In 2013, Mozilla began the experimental Servo project, which is an engine designed from scratch with the goals of improving concurrency and parallelism while also reducing memory safety vulnerabilities. An important factor is writing Servo in the Rust programming language, also created by Mozilla, which is designed to generate compiled code with better memory safety, concurrency, and parallelism than compiled C++ code.
As of April 2016, Servo needs at least several years of development to become a full-featured browser engine.