More than anything else, The Wave acts as a stark warning of the dangers of groupthink. This is where people stop thinking for themselves and mindlessly subscribe to what everyone else is thinking. Groupthink is depressingly common in a number of social environments, especially in high school, where standing out from the crowd is generally frowned upon. This makes the high school setting a singularly appropriate one for the story.
The members of The Wave use groupthink as a means of building and strengthening solidarity in the face of the other students. In their hands, groupthink becomes a dangerous weapon used to exclude those students deemed inferior. It is also used to construct an alternative reality, a parallel universe in which they, and they alone, get to determine who is and who isn't important.
As the story progresses, The Wave becomes gradually more alienated from reality, trapped in a fantasy world of its own making. Groupthink may keep The Wave together, but it also widens the gap between the members of the group and the real world outside, with its moral standards, norms, and conventions.