The moon's orbit is elliptical, and it moves faster when it is closest to the Earth. This is the case for all elliptical orbits, and was discovered by Kepler, who gave a neat rule for predicting how fast an orbiting body moves. (https://kids.britannica.com/students/assembly/view/90830)
For the moon, this means that when it is largest, it is also moving fastest. So the peaks in the graph (where the moon is large) are narrow, as the moon quickly moves away from periapse. When the moon is smallest, it is moving slowly, so the troughs in the graph are wide. It changes size slowly when it is far from the Earth.
The bumps are not all the same size because the orbit of the moon is perturbed by the sun. This changes the amount that the moon changes size. https://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html
When the eccentricity is low, there is less difference in size. When it is large there is a big difference.
This is the cause of "supermoons", when the full moon occurs at the same time as periapse. When the eccentricity is at a maximum, the supermoon will appear especially large and bright.
The Moon's orbit is one of the most complex orbits in the solar system!