Basically, what Pape is saying in this article is that our common views of why people commit suicide bombings is incorrect. We tend to see it as an act of desperation and of religious fanaticism. Pape argues instead that it is a strategically logical action that is not unique to religious fanatics.
Pape points out a couple of important things. First, he says the at the leader in suicide attacks have been the (non-religious) Tamil Tigers on Sri Lanka. Second, he points out that suicide terror campaigns have generally worked to pressure democracies to give in to the terrorists.
So he's saying it's logical to do this (for the groups if not for the individuals) and that liberal democracies need to be sure to avoid giving in so that more groups will not see this as a way to success.