Halo was a middling FPS. Well behind what was available on the PC at the time.
It succeeded because it became ubiquitous. It was the first console FPS with a large multiplayer community, and everyone wanted to play it for that reason.
If hadn't existed, the next decent FPS to come along and take advantage of XBox Live would have replaced it.
Halo wasn't a huge leap in gaming. It was just a decent game in the right place at the right time. Live was the real success story from the XBox, not Halo.
Partly true and partly false.
Halo: CE was revolutionary for consoles. At that point, no one had figured out how to properly map FPS controls to a console controller. There were some previous ham-fisted attempts, but Bungie created an elegant solution to the challenge. This essentially proved to the industry that FPS could be viable on consoles, and Halo's overwhelming popularity paved the road for other developers produce console first person shooters, which is still the most popular genre today. Bungie and Halo are responsible for that, at least more than any other single factor.
That sort of heritage (basically the spawning of the most popular console genre ever) makes Halo a hall-of-fame status game, not "middling" as you stated. But you are correct that it wasn't necessarily head and shoulders above PC games at the time.
Secondly, Halo:CE came out before xbox live. When Live got rolling, Halo:CE wasn't supported. You couldn't play Halo:CE on Live. Its multiplayer was limited to LAN parties, yet it was still insanely popular.
Halo 2 was the first Halo game to be played on Live.
In short, Halo was a big deal on its own merit, because of Bungie's brilliance. It was the killer app that solidified the xbox as a platform. So while I agree with you that it wasn't anything special compared to PC games, I disagree that it wasn't a huge accomplishment in the gaming world. I mean, look at the state of PC gaming today compared to console gaming - it's laughable comparison. Halo and Bungie had a hand in that.
Regardless of what sort of fanboy anyone is - PC gaming, playstation, whatever - it's generally accepted that Bungie is one of the world's best game developers.