A unit of communications hardware or software that is on the same protocol layer of a network as another. A common way of viewing a communications link is as two protocol stacks, which are actually connected only at the very lowest (physical) layer, but can be regarded as being connected at each higher layer by virtue of the services provided by the lower layers. Peer-to-peer communication refers to these real or virtual connections between corresponding systems in each layer.
To give a simple example, when two people talk to each other, the lowest layer is the physical layer which concerns the sound pressure waves travelling from mouth to ear (so mouths and ears are peers) the next layer might be the speech and hearing centres in the people's brains and the top layer their cerebellums or minds. Although, barring telepathy, nothing passes directly between the two minds, there is a peer-to-peer communication between them.