One of the things I worry about with the AP is that at some point some of the players may decide that it is simply better to up and leave instead of dealing with what is going on. I am working on a few different ways to really develop a genuine sense of attachment to the city, both to avoid this happening and to really get the players invested in the story as it plays out.
While designing a few things here and there, I thought I might ask some of you folks if you've ever done anything like this and if so, did it work?
Hopefully, like others have said in their responses to your posts, your players understand their role in the story intuitively. Even if they do however, we as DM's should give them something to really sink their teeth into. All the previous posters have given great advice on this and the only two things I can add are:
a) I did an in-game newsletter "The Korvosa Chronicle" which my players enjoyed and if you search the boards there are details available. This gives you an outlet not only to connect with the PC's but to unload a lot of the background info.
b) Once they connect with an NPC or two kill them off (7-days is a great way to knock off NPC or PC family members / friends) or injure them in someway. This serves two purposes. First, it endears them to the city and her citizens and second furthers their dislike for the villain. My PC's really connected with Kressida. As the villain rose to prominence Kressida and the Korvosa guard's responsibilities and prominence fell. My group disliked that a lot and really rallied behind her.