The Last Kingdom is just a great show in general. One of those top tier shows ala Fargo, The Terror, Better Call Saul, etc. I love the setting/time period, but you can tell from watching the show that you could take the same actors, directors, and production crew and make a great show in any time period.
The characters are written with depth and personality, and the actors know how to bring those things out. While they allow their characters to grow and change over time, they never pull the stunt where someone does something wildly out of character for a plot- convenient purpose.
I think the dialogue is my favorite part. They completely avoid a lot of the trite and tired period bullshit you see with most other shows in this vein. You can tell the writers put a ton of effort into coming up with thoughtful and realistic dialogue rather than just dialing it in with trope-speak.
I could go on because I really like this show but I won't