Disclaimer: I do not in anyway own Castle, just a DVR that allows me to record it and watch it late at night.
Spoilers: Season 2, Episode 18 "Boom"
It's trust. The moment she offers the gun he realizes just how much his detective trusts him.
Detective Kate Beckett is a guarded woman who keeps people out of her heart better than the military keeps people out of Fort Knox. They trade quips because it's safer for her to make fun of him than to take him seriously. After all, if she took him seriously she might realize he loved her.
Trusting him was a step forward; a major step forward. if he could, he would brick the area behind her so she could never step back from this.