it essentially connects two pipes/conduits/cables across an me network.
Say for the sake of a more simple example (although you can use this with me as well, I'm going to use fluids) You have a pump pumping oil, and you are nearby your me network. You can use fluid pipes to transfer the oil through the network via the me p2p tunnel. You first right click with a fluid pipe on the p2p on the side of the oil, to set it to a fluid p2p tunnel (this defaults to ME, if you don't set it) then use the memory card to right click on p2p tunnel.
At the other end you place the 2nd p2p tunnel, and shift-right click on it with the memory card. You can then continue your fluid piping at this end of the tunnel. It's the same principle with the other p2p tunnels.
(I might have mixed up the shift- and normal right clicks - i always mix this up.)