This quote is actually spoken by the character of Charles Marlow in Oliver Goldsmith's She Stoops to Conquer. At this point in the play, the actual "stooping to conquer" is actively taking place. 

Knowing Marlow's inability to feel comfortable among women of his class (upper class), and taking the opportunity that Marlow was confused as to where he was actually staying, Miss Kate Hardcastle pretends to be a modest barmaid to get "the best" of him.

Hence, she is stooping (pretending to be a woman of a lower-class status) to conquer his heart. The results are obviously working. In fact, Miss Kate is so effective in her performance that even her pretend cry goes well with Marlow when he swears that he will never show up in the Hardcastle again. She convinces him by playing her role

I hope, sir, I have done nothing to disoblige you.
I'm sure I should be sorry to affront any gentleman who has been so polite, and said so many civil things to me. I'm sure I should be
sorry (pretending to cry) if he left the family upon my account.

This is the first thing that he likes, and the reason why he says "oh, she weeps". However, he is also struggling with the fact that there is a reality: she is still "a barmaid", and he is still an upper-class man. Although he has a weakness for lower-class women, he knows that he has to shake that off before making official his engagement to the woman who, unknown to him, is standing right in front of him pretending to be a barmaid. Therefore, he says

I can never harbour a thought of seducing simplicity that trusted in my honour, or bringing ruin upon one whose only fault was being too lovely.

Meaning that he cannot flirt with simpler women who think well of him, for he could actually end up taking advantage of such admiration, hence, "bringing ruin" (sex, false pretenses, an impossible romance), to a girl whose beauty would be the cause of his impertinence in trying to court her.

However, Kate has plans. She now knows that there is kidness and seriousness in the man. Now she is really interested in him, especially when she has the control of being who she really is, plus, being the fantasy barmaid of Charles's dreams.

I'll still preserve the character in which I STOOPED TO CONQUER; but will undeceive my papa, who perhaps may laugh him out of his resolution.

Analyze the following quotation from She Stoops to Conquer.

Marlow (Aside): By heaven, she weeps. This is the first mark of tenderness I ever had from a modest woman, and it touches me. (To her) Excuse me, my lovely girl, you are the only part of the family I leave with reluctance. But to be plain with you, the difference of our birth, fortune and education, make an honourable connexion impossible; and I can never harbour a thought of seducing simplicity that trusted in my honour, or bringing ruin upon one whose only fault was being too lovely.

When the audience remembers the title of this play, it is clear that this quote demonstrates how Kate's plan to "stoop to conquer" is showing some hopeful signs of success. Having encountered Marlow in her guise as a servingmaid she finds herself accosted by him. Now, having pretended to cry, and engaging the pity of Marlow, she begins to discover the true character of the man she is meant to marry. Marlow treats her honourably in this quote, and instead of mindlessly trying to take advantage of her and her weakness in this situation responds towards her with honour, sensitivity and dignity. Note for example how Kate responds to this quote in an aside:

Generous man! I now begin to admire him.

However, this is not enough for Kate, and she deliberately tempts Marlow further to prove his honourable nature until he leaves the stage, determined not to take advantage of her and demonstrating his true personality. The importance of this quote lies in the way that finally Kate, and the audience, is beginning to see the true character of Marlow that lies between the two extremes of his behaviour: in reality, he is neither the incredibly socially awkward man who first meets Kate nor the sexually promiscuous man who tries to take advantage of her when she first appears in her disguise. The quote states that he could never "bring ruin" upon her or "seduce simplicity": he has shown himself to be a true gentleman, and therefore ensured that Kate will be willing to marry him.

What is the significance of this quotation from She Stoops to Conquer?

(Aside): By heaven, she weeps. This is the first mark of tenderness I ever had from a modest woman, and it touches me. (To her) Excuse me, my lovely girl, you are the only part of the family I leave with reluctance. But to be plain with you, the difference of our birth, fortune and education, make an honourable connexion impossible; and I can never harbour a thought of seducing simplicity that trusted in my honour, or bringing ruin upon one whose only fault was being too lovely.

The quote in this question comes from Act IV and is said by Marlow to Kate, Miss Hardcastle, but when she is in her disguise as a serving woman. The scene is important because it is when Marlow realises he has not been staying in an inn, like Tony told him at the beginning of the play, and that Kate is not actually pretending to be a barmaid, but is actually, according to her, just a "poor relation appointed to keep the keys, and to see that the guets want nothing in my power to give them." Marlow thus realises how he has been deceived, but as a result, he sees how terribly he has acted towards the father of the woman he came thinking to marry, and feels he has to leave straight away. It is only when Kate feigns tears that he stops and begins to think that he begins to see Kate not as a woman to be seduced and overpowered, but a human in her own right, worthy of respect and consideration. Note how Kate replies to him after this quote is uttered:

(Aside) Generous man! I now begin to admire him.

This quote is therefore important because it signals a change in the relationship between Kate and Marlow, and in particular the way in which Marlow is seen by Kate. Kate's strategy of pretending to be a servingmaid in order to explore Marlow's character and get to know him in a different way, without the formalities that accompany two people of their position and prevent true familiarity, is proving itself to be successful. Marlow shows himself to be a young man who is more sensitive and caring than he first appeared, and a worthy potential husband for Kate.