Loads and support reactions on a beam are balanced internally by resultants that appear when the beam is imagined to be cut.

For a planar beam, two especially important internal actions are shear force $V$ and bending moment $M$.

Cut the beam

Choose a position $x$ and isolate either the left or right part of the beam. The cut face must carry internal forces and moments that keep the isolated segment in equilibrium.

The transverse internal force is the shear force $V(x)$, while the internal couple is the bending moment $M(x)$.

They vary along the beam

Changing the cut position changes which external loads are included in the free-body diagram, so $V$ and $M$ generally vary with $x$.

Concentrated forces can cause jumps in shear, while applied couples can cause jumps in bending moment.

Sign conventions

Different textbooks use different sign conventions. What matters is to choose one convention consistently when drawing cuts, equations and diagrams.

Internal shear force and bending moment are resultants. Later units connect them to the actual stress distributions across the beam cross-section.