Although right now Mozilla Firefox uses the Gecko browser engine soon it will be releasing the Servo browser engine. To be frank I have no idea what different browser engines mean but it must be the architecture like, the Apple line of computers, laptops and mobile devices have a different architecture, the Android line of smartphones and tablets have a different architecture and Microsoft line of computers, laptops and mobile devices have a different architecture. So must be the case with browsers.
If I’m not mistaken, google Chrome and Opera use the same browser engine called WebKit. Again, if I’m not mistaken, the way fonts and images are rendered within your browser window depends on the browser engine being used.
The new Servo browser engine that Mozilla Firefox intends to use has been built using the programming language Rust. The browser will be available for testing in June, according to this Next Web link. According to the official description, Servo is a browser engine that was built from the ground up in the Rust language to specialize in performance, security, modularity and parallelism.
It is being developed for all the platforms including Windows, Linux, Android, OS X and Firefox OS. The functional alpha should be out in June. Developers are already being invited to build applications around the new browser engine and it will be available for public testing in a limited manner soon. The actual normal usage is still many months away.