A comedy of manners is meant to present the typical dynamics of the upper classes while also showing what lies beneath the surface. It is making the "fake" seem real by showing how what seems real is actually fake.
The comedy of manners aims to unveil for the public the superficiality of the rich. It shows the way in which they try to represent themselves as the epitomes of virtuosity and righteousness to, supposedly, set the example for the less fortunate. Meanwhile, behind closed doors, all sorts of chaos ensues ranging from depravity to immorality, lies, and betrayal.
Keep in mind, however, that The Way of the World was new in its kind. Before, theater goers would see a play where the characters were brusque, ridiculous, and foolish. They would be "made fun of" by the audience, and look really silly.
What Congreve did was to craft characters, more than just give comedians some funny lines to perform. In his own words, he wanted to do something a bit more intellectual than merely put people on stage to be funny. When confronted with how fake his play seemed, as it was not a traditional nor typical comedy as the audience expected, his words, as they were recorded, were:
..to design some characters which should appear ridiculous, not so much through a natural folly . . . as through an affected wit . . . which . . . is also false."
He modeled his characters after people that everyone knew or knew "of", and the fact that they maintained a level of dignity really did not sit well among the audiences at first. He also drew a difference between two things: "Affectation" and "Humor". Affectation, according to Congreve is behavior we devise. Humor is that which is given to us by nature. Therefore, we will see both in the play. Previous to it, it would have mainly been "humors" that we would have seen; just plain funny stuff.
This is why the play was received with less than stellar reviews. A modern day scholar can go back now and see that it was not the play, but the audience, that was at fault.
Clearly, these are the situations that take place in The Way of the World. We see the way in which nearly every one of these so-called virtuous characters is flawed to a huge level; how the women conceal their affairs using marriage for their own benefit; how the lovers swap, and how it is all OK as long as it remains hidden. These are certainly the key traits of the comedy of manners, and they are prominently displayed throughout the play.