In Act 3 of The Importance of Being Earnest, Cecily and Gwendolen are furious with Algernon and Jack (respectively) after finding out that both were pretending to be someone that they are not.
In a style that brings out the trivial nature of the play and the silliness of the characters, Cecily and Gwendolen make a quick vow that they will not speak to the men unless they are spoken to first. However, Cecily immediately breaks such vow by confronting Algernon directly about why he pretended to be Jack's evil brother, the fictitious Ernest Worthing.
In typical dandy fashion, Algernon impresses Cecily with a simple answer:
In order that I might have an opportunity of meeting you.
Obviously overtaken by surprise, Cecily consults his answer with Gwendolen, who was previously her number one enemy as is now her ally. Her question is whether Algernon's answer is good enough for her to forgive him. The answer Gwendolen gives her is his answer is only good if she believes him. Cecily then answers paradoxically
I don’t. But that does not affect the wonderful beauty of his answer
This is when Gwendolen responds
True. In matters of grave importance, style, not sincerity is the vital thing.
Gwendolen speaks in reference to Wilde's views on the aesthetic. In an aesthete's view, the superficial, or the appearance of things, is what really matters. Hence, all that is meant to be beautiful, romantic, and exquisite must be taken at face value.
Wilde had no intention of analyzing love and aestheticism in his play. Instead, he used the aesthetic focus to mock the institution of marriage and to expose it for the sham that it is, in his opinion. Marriage is viewed as a shallow, meaningless transaction that is meant to solidify a network rather that to express true love. This is evident in that Cecily and Gwendolen were "in love" with the name Ernest, and in that Algernon had an instant infatuation for Cecily.
Hence Gwendolen is basically telling Cecily that she should accept Algernon's excuse because it sounds dramatic and chivalrous enough for it to resemble a true, romantic apology. It is the way, or "style" that uses, and not the veracity of his words, what matters to the likes of these characters.