s-channel
Two incoming particles annihilate into a single virtual particle, which then produces two outgoing particles. The virtual particle carries the total center-of-mass energy: $k^2 = s = (p_1 + p_2)^2$.
Structure
Two external legs meet at a vertex, producing one internal propagator, which terminates at a second vertex producing two outgoing legs. The internal line carries timelike momentum.
Where it appears
Bhabha scattering (e+e- annihilation channel), pair annihilation into virtual photon, Compton scattering (photon absorption then re-emission).