WOW I was excited to get this so I could TL;DR about my OTP and how I got introduced to Naruto and etc but...no actually it's really hard to explain because a lot of people have already explained the reasons that make this ship interesting and compelling and etc.
I'll try to limit myself to the things that really drive me to like this ship:
So here's the thing--Sakura really, really loves Sasuke. When she was younger, everything she wanted was to have him for herself and it was really pretty selfish but completely understandable for a 12/13 year old. Now, however, she really loves him and it's not just the 'cool' Sasuke, or because he's so strong or anything to do with his history or blood or masks. Post-Massacre, I think that Team Seven are the only people who actually saw the real Sasuke. They got to know him in ways no one else ever has and it's possible no one else ever will know Sasuke the way that Naruto, Sakura, and even Kakashi know him.
Now, I know that Naruto (the series) never stops going on about the special bond that Naruto and Sasuke share, and the understanding and closeness they have of each other, because they share the same pain and the same loneliness, and Sakura never really has. Despite that, Sakura's empathic nature formed a unique bond of her own with him, and her dependence on him, her need for him was something he actually responded to positively because it was something he needed in turn. Because of that connection, he tended to let her in to see glimpses of himself that no one else would ever be allowed. During their time in Team Seven, Sakura was pretty much the closest he'd get to a confidante by the end there, and I think that's really why she fell for him. Sakura fell for the human, the person behind the persona of Sasuke.
After leaving the village, Sasuke locked up that side of him even more tightly, he slammed all his doors and windows shut and bolted it all down even more, and as time has gone on and he's hurt and filled up more and more with rage and hate, he's drifted further and further from the reach of true bonds beyond those he forged with Team Seven. It's been made clear that his bonds with them have not been severed, no matter how hard he tried. At the most, he's 'dropped' them, and can pick them up again at any moment.
....What I'm getting at here is...I don't actually think Sasuke would be capable of letting anyone else in again any time soon, and I don't think anyone else is going to be able to burrow through his defenses either. Sakura and Sasuke have their own special bond, and for Sakura at least that bond is love, despite her better judgment and knowing he's made himself the enemy (but not in such a way that she's delusional and can't recognize that, such as in 635 or when she decides to kill him to save him).
So...really. I'm a fan of 'the only exception'/'the only one'/'slowly cracking the icy shell' type ships to begin with, and Sakura/Sasuke is a pretty big one for all three of those sorts of thing. I could get deeper into the nuances of why I ship SasuSaku and what drives it and all but...yeah...I'd ramble and there are a lot of Sasusaku essays out there that cover it already. (And I don't think you want to hear about how I got into Naruto and how this influenced my starting ships: suffice it to say though, I thought the Sakura/Naruto/Sasuke triangle was going to be way more central to the plot with Narusaku as the forgone conclusion).