Early chrome was driven by the fact that firefox was a piece of garbage. Firefox 3 was not good software, and had an unpleasant habit of totally crashing the entire browser regularly. Your only other popular choice was ie8. Also not great.

Later Google's ability to buy installs and put it on google.com came into play, but for at least the first 5 years and probably longer, chrome was a far faster, more secure, and more reliable choice. They also pioneered the multi-process model to isolate different components of the browser.