Counterterm
A counterterm insertion — drawn as an X on a propagator or at a vertex. Counterterms arise from rewriting the bare Lagrangian parameters in terms of physical (renormalized) parameters. They are not independent diagrams but necessary companions to loop diagrams: the UV divergence of each loop diagram is exactly cancelled by the corresponding counterterm.
Structure
An X marker on a propagator line (mass or field counterterm) or at a vertex point (charge counterterm). The counterterm has the same external leg structure as the quantity it renormalizes.
Where it appears
Mass counterterm $\delta m$ on the electron propagator cancels the UV divergence of the self-energy. Photon field counterterm $\delta Z_3$ cancels the vacuum polarization divergence. Vertex counterterm $\delta Z_1$ cancels the vertex correction divergence, with $\delta Z_1 = \delta Z_2$ enforced by the Ward-Takahashi identity.