Each Feynman diagram represents a contribution to the complex-valued probability amplitudeprobability amplitude that the initial state in the diagram transitions into the final state in the diagram. (What happens “in between” cannot be described classically in terms of particle trajectories.)
Each vertex in a Feynman diagram for a QED process causes an extra factor of the dimensionless fine-structure constant
$$\alpha=\frac{1}{4\pi\epsilon_0}\frac{e^2}{\hbar c}\approx\frac{1}{137}$$
to appear in the diagram’s contribution to the calculated probability for that process, which is proportional to the squared magnitude of the amplitude. This is where the “1% reduction” comes from. Diagrams with more vertices thus contribute less to the probability than those with fewer.
Another way say it is that it is due the fact that the coupling constant between the electron-positron field and the photon field is $e$. In quantum field theory, the electric charge of any particle is a measure of how strongly its field couples to the electromagnetic (i.e., photon) field. Each vertex in a diagram contributes a factor of $e$ to the probability amplitude represented by that diagram, and thus a factor of $e^2$ to the probability itself.