Three things:

It was free, with essentially limitless storage (or that's how it seemed at the time).

The UI was decent, fast, with no page reloads -- it felt responsive, like a native app.

Google seems to be the first to really leverage the large number of their accounts to catch spam more effectively than the other providers. You basically got no spam from GMail in the beginning.

Yahoo and Hotmail were both super clunky in comparison: slow, ads, more spam. It really was no contest.

And then Android just meant nearly everyone got an account ...