In this book, Gitlin is arguing that we modern people are inundated by media. We face a torrent of media that we must all deal with in one way or another. He argues that there are three broad ways in which people deal with this media overload. One of those ways is by becoming "exhibitionists."
The exhibitionist, Gitlin argues, embraces the media torrent and tries to become a willing participant in that flood. Exhibitionists are the people who really want to be part of something on TV. These are people who are willing to go on talk shows or are willing to have their case decided by some TV judge. They are the ones who allow cameras in their homes for reality shows.
Exhibitionists, then, are those who cope with the flood of media by embracing it and becoming part of it.