@Nenous fellow forumites already gave you a good enough description and I don't have something significant to add on them. So I'll link you to the gameplay footage that was released (not as snippets, but as an actual playing session). You were told about the atmosphere and story, maybe this will help you form an impression of how it's actually played.
Something to note about these two videos I'm posting.
(1)
The combat: The player demonstrating, in both of them, is playing very carefully. He jumps in to attack, and jumps right back. This makes the combat seem jerky at times and not too fluid, but that's not the case. It's simply because of his
playstyle. One of the two videos in my post is a 35-minute section, played in English, with the same sort of cautious fighting style.
However, CDPR released two additional videos, replaying the exact same sequence, only in Polish and Russian. Thing is, in those two different videos, the player that demonstrated played much more aggressively. He didn't retreat after every strike of his and stayed in the thick of things. This made the combat much more beautiful because attacks were chained together and you could see many more different animations. And it has a lot of them, more than any melee game I've seen. I didn't put these two different videos here because I don't want to overwhelm you with material, but if you want we can easily link you to them to get a better feeling of combat.
The English version is still recommended for the first watch due to the Developer narrating and explaining a bit about what's going on.
(2)
The Visuals: These videos are many months old, and at their time they were already using a build of the game that wasn't their most updated. Meaning that TW3 might look better today (or it might not, who knows).
This is from E3, run on XBox.
[video=youtube;BivVXw-NLTw]https://www.youtube.com/watch?v=BivVXw-NLTw[/video]
And this is on PC:
(If you have the patience to download, you can find the 35-minute video
here in sharper quality than YouTube's)