This isn't even the whole story arc. It's just its first half, followed in 2019-20 by Sword Art Online: Alicization: War of Underworld. Both Alicization series put together cover almost fifty episodes and volumes 9-18 of the light novel series.
Unsurprisingly, given this level of ambition, the show's pretty serious. It's dramatic, epic and often intense. It has almost no sense of humour, but it's adapting the story sincerely and faithfully. Its only noticeable flaw is, I suspect, due to that fidelity. There are a few points in the series where our heroes are fighting to the death against an extremely powerful enemy... but when the narrative calls for a tear-jerking emotional scene, that enemy will seemingly take a coffee break. Final farewells? Sure, take your time. Preparing a potentially table-turning counter-attack against that very same enemy? Yeah, that's fine too. Amusingly, though, a couple of minutes later, the episode will remember that the enemy exists.
In a print medium (novels, manga), that kind of thing can work. Time proceeds at the reader's pace, so one suspension of disbelief isn't as stretched. When you're watching it on a screen, though... sorry, nope. For what it's worth, this happens in ep.4 (goblins) and eps.22-24 (Administrator Quinella, although on one occasion it's given a dialogue justification).
Oh, and I didn't believe ep.15. The backstory with the little girls is horrifying and extremely strong, but I didn't believe in Kirito's gambit. That's a choice for the sake of drama, rather than for making sense for the character and the situation.
Anyway, the plot. Kirito is living in the real world and planning his future with Asuna... but he's also an amnesiac peasant in a fantasy computer game world. Don't worry, it's explained. He's both. The problem with MMORPG anime in general is that a game's a game, so it doesn't really matter. Here, though, the fantasy world's inhabitants have no real world equivalent. They're an experiment in AI, grown naturally from computer-translated souls in a time-accelerated world that goes a thousand times faster than ours. It's called "Underworld" and for its inhabitants, it's existed for centuries.
Kirito is one of those inhabitants and he can't log out. He's going to grow up there, from childhood. He'll make friends, declare his intention to be a swordsman and set out to rescue them when bad things happen.
I like the scale. Many years pass, in a world with its own geography, social structure and even physical laws. Kirito starts out as a nobody. When he starts training as a knight, he's not Instant Superman but instead can't even beat his tutor. There's also a dark bit of worldbuilding in that the locals are incapable of breaking the law. If they try to disobey an order from a lord, for instance, their bodies seize up and their right eye explodes. This is taken somewhere horrific in the infamous ep.10.
The world's big bad makes sense. In a computer world, she's got administrator privileges. She's made herself immortal, beautiful and nude (but with Godiva hair).
It's a classical fantasy epic, but with a virtual reality underpinning. It's not just an ego-stroking hero romp, instead making Kirito work to earn his victories against intimidating enemies and real dangers. Ep.17 made me go "yikes". (He's going up a tower the hard way.) Our heroes are likeable, while the baddies can be vile. I'm looking forward to Part 2.
(Update: Part 2 is excellent and in combination I'd upgrade my view of this first half too. The whole series is top-drawer.)