I will add a few more details for new players, to establish expectations and set the tone:
-No, you don't need to play The Witcher 1 or The Witcher 2 to play this game. This isn't Mass Effect 3 where the point of the game is to finish the story of the previous two parts. TW1 had a separate story, TW2 had another separate story. The only thing you need to know is that a Southern Empire has invaded the place where the stories always occur in the games and books, the Northern Kingdoms. Geralt himself is usually politically neutral, he doesn't care if king A or king B rules, so this isn't even very important for him.
-No, you don't need to know who the heck are some characters called "Ciri" or "Yennefer". Her screen times in Witcher 1 and Witcher 2 are.. zero. So you will be in the same conditions as other players.
-The Witcher games have a strong focus on story, so even if this sequel is open world, don't expect something like Skyrim which has a plot but lots of people play it living random adventures as they explore. Even if they have done the exploration well in the game, a good part of what makes the game will be the story and writing in general.
-The main character, Geralt of Rivia, is a character with an established name, an established profession and even a somewhat predetermined personality, so don't expect a game where you can choose if being a great asshole or a super paladin, or choosing between being a sneaky thief, an archmage in a tower or a warrior that is also a vampire. Yes, you can level up the skill tree in magic, sword or alchemy but you will be still a witcher, a skilled swordman who crafts potions and use some magic here and there.
-You may heard Geralt is a mutant. Though basically human, witchers are manipulated with secret formulas as a child to give them their enhanced physical prowess and general aptitudes to do their profession, a monster hunter for hire.
Said mutations leave them sterile, which is an important point to make as in this game will establish Geralt's relation with a "foster daughter" figure.
-Being in medieval times the general populace isn't very kind and open minded, so they call witchers "mutants" and "freaks" and other not so nice names. They are disliked in general, though they are tolerated because their utility for society as monster hunters.
Book Note: in the books this point is even more marked, in the video games is there but just for a bit of flavor.
-In fact this isn't a "heroic fantasy" setting, but a "low fantasy" setting, where life is cheap, people are poor, ignorance and hatred rules, etc.
Book note: In fact the first two books are all about the idea of taking usual situations of fairy tales and give them a "realistic" twist showing how different things would be if the setting and tone would be more like real life. Which reminds me, in the books Geralt is poor, his "Roach" is usually a cheap used horse or a mule, he is more really a traveling hobo working here and there.
-Monster hunting. Killing an important monster isn't supposed to be straightforward. Witchers study their prey, they research about their behavior and weakness, and prepare for the combat crafting and drinking the right potions. Book note: witchers use barely the most basic magic in the books, in the other hand they are supposed to be good alchemists, this is proved in the creation of witchers themselves with special potions, and in the preparation of their potions for combat or other uses.
But be careful, you receiving a contract to killing monster X doesn't mean X is really a monster. There will be times the "monster" is a sentient creature, so maybe you can negotiate with it.