It is always important to examine the context of a quote before trying to work out its precise meaning. This quotation comes from Act III and is said by Kate to her maid as she disguises herself as a servingwoman before going out to meet Marlow again. She has already met him one in her normal clothes, and was met with timidity and crippling shyness from Marlow, who is the man that her father intends her to marry. However, she has also been intrigued by the reports of her father about his very different behaviour towards him, where he has appeared to be brash and arrogant. Kate gives three reasons for her behaviour, and the first acknowledges her own beauty:
In the first place, I shall be seen, and that is no small advantage to a girl who brings her face to market.
What is important to note is the use of the word "market," which shows how Kate recognises that marriage was about bringing your best strengths to the "marriage market" and exhibiting your beauty in order to attract the attention of men. This ties in with Goldsmith's satire on marriage, as he argued in marriage women were viewed not as individuals in their own right but only in terms of the assets (wealth and beauty) they could bring to that marriage.
Secondly, she hopes to get to know Marlow, which, as she comments, would be an achievement given that he only is familiar with servingwomen. Lastly, she wants to take Marlow "off his guard" and survey the scene before launching her attack on him. What is so key about this quote is the way that the audience sees Kate's plan unfold. She is going to take the initiative and make an effort to approach Marlow on her own terms, thereby, as the title indicates, stooping to conquer, or lowering her social rank in order to gain her husband.