Kate Beckett is exhausted, as she is the only police detective ever available when a murder takes place in New York City. She loves that mystery writer Richard Castle is shadowing her, but also understands that the show's writers have to prevent a relationship from developing too soon, since happiness is boring.
Her favorite pastime is saying, "Castle, you're staying here!" in every episode and then feigning surprise when he ignores her. She has some Major Issues stemming from the unsolved murder of her mother, and the 589 button-down shirts and 67 cropped leather jackets she owns symbolize the walls she has constructed to prevent her from getting hurt again.
Beckett seems too young and too beautiful to be a real police detective, which is probably a sexist thing to say, but those are exactly the sort of statements that drive her.