"They let me pick, did I ever tell you that? Choose whichever shooter I thought was the best on the Xbox 360.
You know me. I did my research. Watched as you became the game we needed you to be.
Like the others, you had great gameplay and art style and narrative: A natural contender. But you had something they didn't. Something no one saw… but me. Can you guess? Luck."

Well, maybe it was not luck, and I'm just being cheesy here misquoting that Cortana speech from the beginning of the game.
But Halo 3 and the series in general definitively has SOMETHING, even if you can't grasp exactly what that thing is. Almost 3 years after the game was released it still ranks among the top playable games in the Xbox live charts.

So what is it exactly that caught so many gamers who come back to play this game over and over? The responsive gameplay, and those magical 30-seconds-of-fun repeated over and over? Or maybe the refined weapon-vehicle sandbox which makes every encounter interesting to tackle? How about the inclusion of innovative and accessible ideas like Forge and Theatre, who let the community go wild with what they can do with the game? Or the core campaign itself, which lets you go through it alone or in 4 player co-op for enormous replay value? Not to mention the endless support from the team at Bungie, who continuously offered new tweaks to keep the game balanced and released map pack after map pack so the multiplayer remains fresh even two years from the initial release?

It's probably the whole package then. There might be other shooters who cater more to your taste in terms of story, gameplay or presentation, singleplayer or multiplayer. You might not even "get" the whole fuss around this game because you had a better experience with some other game.
But Halo 3 does just about everything, and it does everything right – Combat has indeed evolved and evolved again (and it is still evolving judging by the Halo Reach beta). Right now, Halo 3 probably offers one of the most (if not THE most) complete and most satisfying experiences on the Xbox 360 – at least until the next iteration is out.