The Event CG is both a central part of the story and potentially the single most expensive part of any given visual novel (at least, that's the way it is reported). A lot of visual novel makers include their number of Event CGs in their advertising, and often the final Event CG for a route becomes the defining memory for the reader. The CG above, from Tokyo Babel, is one of a number of defining moments, where hints of the reality that lies behind the facade, become evident, even as the characters battle to fulfill their desires.
Poor utilization of Event CGs can often result in the wrong scenes being emphasized or major plot twists being overlooked, because VN readers are trained to associate them with story progression. On the flip side, effective use of an Event CG can give life to even a trite or mundane plot. Despite the fact that I often made fun of 'charage' (the standard sol-focused VN that had a strong focus on character development but lacked overall cohesion), this was one aspect a lot of companies excelled in. A single Event CG at exactly the right time could turn a mundane romance into a dramatic, emotional one that feels more real to the reader (and I'm not talking about H-scenes, though I'll get to those in a moment).
Now, for the more controversial aspect of Event CGs... the H-scene CG. To be blunt, in the vast majority of plot-focused visual novels, sexual content is neither necessary nor does it add anything, save that if there wasn't one, a lot of readers would think they were missing out. However, for a lot of romance-focused visual novels, experienced VN-readers feel cheated if there isn't an H-scene, even if they don't necessarily want to watch/read it.
Rarely, a visual novel makes the H-Scene a vital part of the story progression, and in these cases, it is easy to feel that it was a valid choice. Devils Devel Concept's H-scenes (the majority of them, anyway) usually have a role in how the story comes to life, as the protagonist's near-emotionless persona tends to crack open the most in these scenes, and the author does an excellent job of portraying the way his way of thinking and that of the heroine don't quite match. Similarly, Draculius's H-Scenes reveal a great deal about the characters and setting that would otherwise be missed by the reader. The Event CGs, in these cases, have innumerous variations in expression that go along with the text to bring the characters, their emotions, and their desires to life in a way that can't quite be expressed without them.