They are referring to the sun being eclipsed from the GEO satellite as it passes through the Earth's umbra. If the GEO satellite does not have enough battery reserve, it will need to stop broadcasting temporarily.
The sketch makes it appear eclipses would occur every orbit. But the satellite's GEO is aligned with the Earth's rotational axis, not its orbital axis. As a result, the satellite's GEO orbit is not coplanar with the Earth's orbit. Satellite eclipses are most frequent and last the longest during the equinoxes. The same is true of lunar eclipses, for similar reasons.
Eclipses are not limited to geosychronous orbits. Non-polar LEO satellites are "eclipsed" for less than 50% of their orbit when they pass over the Earth's night side. The sketch below shows the relationship of umbra (total eclipse) to the penumbra (partial eclipse)
The next sketch shows a satellite with a LEO perpendicular to the terminator (sunset line)
As the satellite progresses a-b-c,, the intensity of solar radiation on the panels decreases.
The next sketch shows a satellite with a LEO coplanar with the terminator. It experiences no eclipse
You can observe the LEO eclipse yourself. Pick a low-inclination satellite travelling west to east across the evening sky. At some point, after passing overhead, it will dim as it passes into the penumbra, then disappears quite suddenly as it hits the umbra. If you follow a succession of satellites, you will notice the "line of disappearance" is roughly along a celestial meridian. The line will slowly march westwards until midnight, when there will be no visible satellites. Then satellites will start appearing in the eastern sky.