I would say the bulk of it is ease of administration, and, as others have mentioned, the ability to get it up and going and use quickly and simply while having a relatively opaque understanding of how an RDBM works underneath.
The other major difference is that MySQL AB put a lot more effort into having an extremely concise, easily navigable and user-friendly online documentation repository and associated support community. Postgres has since made good strides in this area, but a lot of the documentation still reads like something intended for a fairly specialised audience that more or less knows what it wants; the ignoramus-friendly parts of MySQL's documentation are a lot friendlier.
For this and its administrative simplicity, it just got to be known as the quick and easy database, and Postgres as the rocket science database. (In reality, this is not true; only Oracle is the rocket science database. :-)
Also, MySQL was/is more appealing to corporate adopters since an Actual Company(TM) is Behind(R) the project. Postgres has a commercial footprint in the form of various third-party consultancies like CommandPrompt, but the core of the project is a Debian-like anarchic band of hackers. Nothing turns corporate America off more than a bunch of long-haired GNU hippies when it comes to big-ticket stuff, though they begrudgingly put up with it for Linux by now, Linux having become somewhat "legitimised" by the backing lent to it by IBM, the existence of Redhat, etc.