Romantic comedy films are a a sub-genre of comedy films as well as the romance.
The basic plot of a romantic comedy is that two attractive people meet, banter with each other, but despite an attraction obvious to the audience do not become romantically involved because of some internal factor (on the surface, they do not like each other) or an external barrier (one is romantically involved with another person, for instance). At some point, after various comic scenes, they are parted for some reason. One or the other partners then realises that they are perfect for each other, and (often after some spectacular effort and/or incredible coincidence) they meet again, they declare undying love for each other, and disappear off into the sunset together.
Of course, there are innumerable variations on this basic plotline. It is not even essential for the two lead characters to end up in each other's arms: My Best Friend's Wedding is a good example.
The basic format of a romantic comedy predates the cinema by centuries. For instance, many of William Shakespeare's plays, such as Much Ado About Nothing, fall squarely within the bounds of the romantic comedy.