For myself, I came across The Witcher quite by accident. I was browsing GOG.com, and noticed an RPG which was not a cartoon, nor featured a muscle-bound pinhead, wielding a blade twice his size, nor a young, inexperienced peasant as the protagonist. The setting appeared refreshingly serious, realistic enough, measured in its proportions, and mediaeval, yet was still fantasy. Intrigued, I gave it a whirl. Granted, there were elements and locations which did not always appeal to me (Wyzima and the Swamps can become rather wearisome after a while); however, the music, the story, attention to detail, and, of course, the character of Geralt impressed me.
What intrigued me most, though, was the concept of witchers: Professional monster-slayers, created to defend humanity, and endowed with the power to do so. The question of how Geralt should use that power, and his responsibility as an individual possessing it still fascinates me. This shone out from amidst all other aspects of the story and its world.
The Witcher has often been described as 'uniquely Polish' in its atmosphere. I still don't know if this is true or not (since I'm no expert on Polish atmosphere). Yet, to me, as a mediaevalist, the game seemed to have a recognisable, grim mediaeval European environment, which appealed to me. As I played, I recognised motifs and references to tales, myths, and legends from across Europe which I knew from my studies. Even if there were numerous modern elements thrown into the world -- often humorously -- these didn't detract terribly from the atmosphere. The developers had crafted their world well. In particular, the music helped to build and maintain a sense of location -- a spirit even -- especially in the Outskirts, and at the Lakeside.
As others have observed, the Lakeside and Murky Waters were a memorable reprieve from the plague-ridden Outskirts, embattled Wyzima, and the monster-infested Swamps. The Lady of the Lake's domain shall remain one of my favourites, as will her character, not merely because of her place in Arthurian mythology, but also for the enchanting aura which surrounded her. Her gift to Geralt, and the oath which accompanied it, elevated the White Wolf into another, higher realm -- a realm I knew very well.
All in all, a combination of mystery, music, setting, ethical questions of 'heroism', and an engaging tale captured, and held, my attention in The Witcher, and made me curious to learn more. . .