I could go into a massive essay about how the haters are just hating, and listing point by point all the things the Halo series did spectacularly right, but in order to save on space, I'll try and limit it to a few key points.
Firstly, you have to look at the context of the time. Before Halo, the only console shooters that anyone had even heard of were Goldeneye, Perfect Dark, and Timesplitters. And while Goldeneye and PD were instrumental at getting FPS's onto the consoles, they were hardly without faults. Certainly in the control department, Goldeneye and PD both now handle like complete arse, thanks in no small part to the unwieldy N64 controller and its single analogue stick.
Halo, along with Timesplitters, showed that you could make a first-person shooter that not only worked on a console, but worked beautifully. Moreover, where Timesplitters was almost entirely focused on multiplayer, Halo CE had a massive single-player campaign unlike anything else at the time. FPS' at the time were still largely enclosed, corridor-based affairs. Halo used that template for the opening level, then proceeded to throw the player into a wide, expansive world full of epic levels. This was a game where vehicles could freely be commandeered in order to get from one side of the level to the other. Perhaps most importantly, it was a game that had absolutely brutal AI. For the time it was released, Halo's AI was absolutely top-of-the-shelf, boasting enemies that exhibited all sorts of adaptive behaviour depending on how the player acted.
Secondly, Halo was one of the first, and to this day still one of the only, shooters to focus on emergent action as opposed to scripted set-pieces. In order to understand what I mean, you really need to compare it to something like Modern Warfare. In the Modern Warfare games, action in the single-player game is largely scripted, and revolves around pre-arranged set-pieces that deviate very little from playthrough to playthrough. They allow for bigger bangs and more spectacular sequences, sure, but they also get very repetitive after more than one playthrough. In contrast, action in Halo is largely non-scripted, and is defined between the Covenant/Flood AI and the player's actions. While this means that Halo usually lacks the spectacular set-pieces of the COD games, it allows the player to create their own set-pieces, using the game's mechanics as tools with which to do so. If you want to run up to an enemy tank, plant a grenade, then escape away on the back of a friendly Warthog before it blows up, the game will allow you to do so. Alternatively, instead of grenades, you may want to ride shotgun in said Warthog while AI (or preferably a co-op teammate) drives, using a rocket-launcher to take out the tank while your team-mate drives the Warthog over a spectacular jump. Or you both may decide to ride Ghosts instead, making a convoy that destroys the tank through sheer relentless firepower.
That is where the real joy of the campaign, and indeed multiplayer, resides. Being able to pull off crazy stunts and action sequences, not becase the game scripted them, but because you wanted to see if you could pull it off. That's something that even modern shooters rarely allow for.
Lastly, Halo 2 standardised online-multiplayer for console FPS's. After Xbox Live was released, but before Halo 2 came out, online shooters were a weird mish-mash of ideas. Some games would have some features, others would have others, but none had what we would recognise today as the fundamental basics of online multiplayer. Halo 2 was released and not only offered the best online action of any shooter at the time, it also standardised how games should go about handling their multiplayer. Every online shooter running on a console today owes a debt to Halo 2. That game was the single most important multiplayer shooter since Unreal.
Ultimately, it's one of those "You had to have been there" kind of things. You need to imagine a scene without Call Of Duty, Resistance, Killzone, Gears, Half-Life 2, Bioshock, etc, in order to appreciate what Halo brought to the table. At the time Halo came out, Half-Life One was seen as the pinnacle of the FPS genre. That's how far back we're going.