Private Peering
Definition: Private Peering is Internet Peering across transport with exactly two parties connected to it, usually a fiber cross connect or point to point circuit.
Most Internet Exchange Points offer or facilitate the interconnect of two parties using some form of dedicated point to point interconnect known as cross connects or circuits in addition to offering a Public Peering fabric.
See the Great Public vs Private Peering Debate for a discussion of why some prefer private peering. One attitude expressed was that the ISP wanted no active components to break between them and their peer.