What is Gmail? Of course, the easy answer is that it's a webmail system that set a new standard in the amount of space available to users - 1 gigabyte each. By comparison, most other webmail providers (eg Hotmail, Yahoo) were offering between 2 and 10 megabytes. Most of these have now increased their offerings to up to 100 MB, still not as much as Gmail but more than enough for most things. But hey, diskspace is cheap.
Gmail also has some clever (read intrusive) processing that allows them to target ads specifically at you. This can be good and bad - at least the ads are targetting at you. But there are privacy concerns. That said, if anybody is storing confidential data on a remote webmail server, they need to think about that first.
Gmail is more than this though.
Gmail is, in my opinion, a huge marketing experiment.
Mail services come and go. Some are better than others, and Gmail is one of the better ones. And if they had sent out announcements, put it on the google.com website, it would have taken off slowly.
By making it "by invitation only" (who got the first invitation?), it makes it special. Kinda like Orkut. Which is also owned by google. It made people want to have a Gmail account, just so they could say "Hey, I've got gmail, I've got invites, who wants one". And by getting people onto it, they get more people they can target ads to, and therefore more money they can raise from their sponsors.