-webkit- and -moz- here are called vendor prefixes; they generally indicate a browser-specific feature of CSS, or one that’s under development/still a draft and can’t be considered a standard yet. When these features are used “ahead of time”, the only way to make it work in every browser is sometimes to provide a different rule with a different prefix for each one — that’s what you see in the project. The idea is that eventually, though, the feature will be standardized, browsers will drop the prefixes, and life will go on.
-webkit-gradient, for example, was the first way to define a gradient in CSS, but was replaced by a completely different linear-gradient and radial-gradient syntax.
A convenient way to find out what browsers support a certain feature and what prefixes you need if you’re using it before a definitive standard or global unprefixed browser support is Can I Use….
Some common prefixes are:
-webkit- for WebKit-based browsers, including Chrome/Chromium and Safari
-moz- for Firefox
-ms- for Internet Explorer (9 and up)
-o- for Opera (pre-WebKit)