Similar in use to the BHC, or one way backhaul check. If an intermediate point has a higher fare than the origin and detination fare (and a stop over applies at that point) one would subtract the current fare from the higher intermediate fare, then add that on to the price of the ticket.

It is to prevent people from the "hidden city" ticketing that was so prevelant in the US years back, although these HIP and BHC rules are part of international (not domestic) fare construction.