What the Nurse is telling Romeo here is that she will tell Juliet that she (the Nurse) believes that Romeo is going to deal fairly with Juliet.
In the part before the lines you cite, the Nurse criticizes Romeo and warns him that he had better not be toying with Juliet. She tells him that Juliet is young and that no gentleman would toy with her.
Romeo tells the nurse that he protests her attitude -- that she's not being fair to him. So then (the part you're asking about) the Nurse tells him that she will tell Juliet that he did protest her words. She says this proves that he really is a good guy.
Juliet is supposed go to Friar Laurence's cell. She can do the sacrament of confession and then they'll be married.
It's difficult to know exactly what portion of the conversation you mean, since most editions of the play have different line numbers. For example, in the etext version here on enotes, both the Nurse and Romeo speak in these lines. So I'll discuss the conversation from the Nurse's longer scolding of Romeo.
At this point, she is upset from Mercutio's taunting. Although Mercutio exits, she is still flustered, and a little angry that Romeo would choose to associate with someone who would make sexual comments to a woman. She first warns Romeo not to "lead her(Juliet) into a fool's paradise"; essentially, she tells him not to lead her on, or play around with her. She makes it clear that she thinks Juliet is too young, and thus if Romeo "deal[s] double with her", it will be a great wrong on his part. This upsets Romeo, who asks the Nurse to say only good things to Juliet about him. However, the Nurse misunderstands his use of the word "protest", which leads to a few confusing moments between the two of them.
Romeo quickly recovers, getting straight to his point: how to ensure that he & Juliet will be married. He tells the Nurse:
Bid her devise some means to come to shrift
And there she shall at Friar Laurence’ cell
Be shriv'd and married. Here is for thy pains.
So, Juliet will make up some reason to go to confession with Friar Laurence, but in reality she & Romeo will be married. Romeo also asks the Nurse to prepare a rope, so later that night he can climb up to Juliet's room to consummate their wedding.