Specifically, it was Phoenix (aka Firebird, aka Firefox) that made that happen: a version of Mozilla that threw out everything but the browser, including the mail client that jwz considered essential. It made it smaller to download and faster to run, but most importantly it made it faster to write: they could ship improvements to Firefox way faster than they could to Mozilla, simply because there was so much less of it.
Yup. A classic example of minimum viable product (although for phoenix far more than minimum). Phoenix was a breath of fresh air back then. Mozilla was as bloated and cumbersome as Netscape ever was, but Phoenix was fast, streamlined, and a joy to use.
The turning point was when the RSA patent expired and Phoenix could fully support SSL out of the box without any wonky add-ons. At that point there was no longer a good reason not to use Phoenix/Fire{bird,fox} and it started gaining huge amounts of momentum.