I think for me, it's that I tend to gravitate towards intellectual characters, which Solas appears to be, and that's what first made me want to learn more about him.
I'm also very interested in the concept of the knight errant - the idea that someone has their own morality which may or may not agree with the "law," and they go around on adventures helping people. Think Robin Hood, or Yojimbo, or Wuxia films, or even a lot of comic book superheroes (it's one of my favorite literary tropes, I use it all the time). In the interview about Solas, we learned about his "more complicated than that" ideas on right and wrong, and so that made me think of the knight errant concept.
And then of course I found out that he has the same writer as Mordin, my favorite Mass Effect character!
Everything I've learned since then only strengthens my interest in him. Mr. Weekes keeps hinting at all these things that fall right into my favorite nerd-cred zones. For example, I never thought my Shakespeare knowledge would help me speculate on a video game character!
Really looking forward to the game! All the characters sound so interesting, and Skyhold looks amazing, and hours upon hours of story and exploration... I just hope I get the funds together to build my new PC, or else my copy of the game is going to be mocking me for a little while!