Basically, Mozilla stands for "Mozilla compatible" while "KHTML, like Gecko" describes the rendering engine.
Essentially, Chrome's user agent string is saying "I'm compatible with Mozilla and my rendering engine is like Gecko" as a way of describing itself to developers.
Most (if not every) browser will identify itself as Mozilla-compatible as a kind of legacy thing, regardless of affiliation with the Mozilla foundation. Yes, even Internet Explorer.
More info on strings in general at: Mozilla's developer center.
Also, if you're developing based on user agent strings, don't. You'll only find yourself in a world of hurt: browsers get upgraded to implement features and your user agent sniff might still exclude them, user agent strings can be spoofed, and good old Opera likes to report itself as Internet Explorer in older versions.
Instead, use feature detection to determine if a feature you're trying to use exists for a given browser and then use it or don't.