She's relatable because she was put in an awful situation she had no control over and tried to survive it. She was completely alone and sold by the only family she's ever known. Yes, I think she is inspiring and personally I think she's relatable.
I think many people have been through some terrible moments in their lives when the only thing they could do was to find strenght within themselves to make it through another day. And that's basically Dany's struggle in book 1 and her inner thoughts throughout that book. After that we're just watching what she's becoming, and going after the only purpose she has left, considering her lineage.