The external legs (propagators) of Feynman diagrams represent real (not virtual) particles, whose interactions we want to study. Virtual particles run in the cl

The external legs (propagators) of Feynman diagrams represent real (not virtual) particles, whose interactions we want to study. Virtual particles run in the closed loops of Feynman diagrams, i.e. they can be thought of as actual particles (of the same or of other types), being created by the collision of the real particles, and they recombine back into the real particles. So say two real particles collide and scatter off each other: the collision creates all kinds of "virtual particles" that are allowed by the interaction terms in the theory Lagrangian, and they recombine back into the same two real particles because of the same interaction terms. Using the famous Feynman's path integral, you integrate over all possible virtual particles and their states (with different contributions to the integral), normalize those contributions, and then you get the probability (or amplitude) of the real particles with a certain state getting scattered (or transitioning to "another [quantum] state") - the external incoming and outgoing "legs" of the diagram.