Daenerys wasn't a hundred percent sure about Varys' loyalty, since it was him who betrayed King Robert Baratheon, whom he had sworn to serve. She was wondering what kind of servant would do that. Varys answered that he would always serve the realm in the first place (as he told Ned Stark before). He will never serve a King or Queen with blind loyalty. He will always use his eyes and draw the consequences, if he must. Though he will also serve Dany as well as possible, because he knows that she was the best chance for the realm. Dany made him swear that if he ever thinks she's failing the people, he won't conspire behind her back. She obligated him to look her in the eyes and always be honest with her. Varys swore to do so.