Box
A closed loop with four vertices forming a quadrilateral. Four internal propagators. The simplest topology for four-point functions at one loop.
Structure
Four vertices connected cyclically by four propagators. External legs attach at each vertex. For light-by-light scattering, four photons attach to a closed fermion loop.
Where it appears
Light-by-light scattering ($\gamma\gamma \to \gamma\gamma$): a closed electron box with four photon legs. UV finite by gauge invariance. Gives the Euler-Heisenberg effective Lagrangian at low energies.