I never ever got what supposedly was so "redefining" or amazing about Halo. I played it when it came out for the PC, and nothing felt that special about it. Don't get me wrong, it was a really good game, and I enjoyed it immensely, but I never got the hype surrounding it.
Story driven FPS? Half life did that. First good FPS on consoles? I'd argue that was GoldenEye, Vehicles in an FPS? Starsiege Tribes in 98, and I am sure there were others even before that. Multiplayer? Doom, Quake, Counter Strike...
In fact, I recall that it dumbed down streamlined things that I was used to from other games, and I wasn't impressed with that.
Maybe it's because besides playing on consoles I was always an avid PC gamer, and it just didn't offer anything new for me, whilst new gamers, especially on consoles, were introduced to brand new things.
People don't remember what Halo did because what it did was so natural it got retconned into always existing and it becomes too obvious to give them credit for it(and that's before someone tries to disprove it by finding an unreleased MSX game that had a similar feature all the way back in 1987, and therefore Halo didn't do it and the retconn is correct).
As a whole it's just a first person shooter, some of the components are where it gets innovative.
Vehicles was one thing, they had existed before, but the way they controlled was new. Get in the warthog, look backwards, press forward and the car will solve how to best turn and head in that direction. It was indirect steering, you point and it takes you there. Doesn't sound like much but it was a new idea, when fleshed out further you get the auto-navigation of obstacles seen in Assassin's Creed.
And Galleon in between those two, it's a game much closer to AssCreed and back then(2002-ish?) previews sometimes described how the movement worked by comparing it to the Warthog in Halo, point-and-go. (Seems silly for a third person game, therefore Halo didn't do anything.)
Grenade on a button, making them useful. Not every game adopted it immediately. People thought Valve were complete retards for having the grenades in the weapon menu of a huge big budget game like Half-Life 2.
Melee on a button, making it useful. Why even have melee in a game if you have to cycle through every weapon to get to a weak-ass punch? (Duke3D had a melee button for the weak-ass kick) Not every game adopted it immediately. People thought Valve were complete retards for having the
grenades crowbar in the weapon menu of a huge big budget game like Half-Life 2.
It wasn't just that melee was put on a button, it also had a real use and gameplay implications. Instead of dealing 5 damage to an enemy that didn't flinch when repeatedly punched in the face it knocked out enemies if the player remained undetected or it could stun/stagger them in combat. I think the shield dudes staggered if their shield got smacked so rushing them was sometimes a good idea. Imagine rushing enemies with the crowbar and thinking something good will come out of it...
How many games have a button for grenades(or special attack) and a meaningful melee, like the knife in COD, these days?
There's much more, usually quality-of-life innovations that makes the genre as a whole better. Halo isn't the only game like this, there's more. Metal Gear Solid 1 is one where people overlook a lot of what it brought to the table at the time.
