The generated power is, among other things, a function of the number of photons that strike the panel per square meter per second (the photon flux), AND the wavelengths (the "colors") of the photons that are striking the panel.
A photon's wavelength determines its energy. When a photon strikes the solar panel's surface (the silicon material), if the photon has the right amount of energy the collision knocks loose (it "ejects") an electron from its silicon atom. *Fun fact: Albert Einstein received his Nobel prize in physics for understanding and describing this photoelectric effect. The liberated electron (-1 charge) and the ionized silicon atom (+1 charge) now form a kind of battery. This is a GROSS oversimplification, but hopefully you get the idea.
Only certain photon wavelengths have the required energy to eject an electron from its silicon atom. Unfortunately, Earth's clouds are very effective at absorbing and reflecting those particular photon wavelengths. Therefore, when a cloud passes between the sun and the solar panel, fewer photons strike the panel per square meter per second (the photon flux reduces), and therefore there are fewer ejected electrons per square meter per second, and therefore the panel produces less power.
The panel's output power is the product of its output voltage and output current. So if the output voltage remains constant and the generated power drops due to reduced photon flux, then the output current must drop:
P = I\,V \Rightarrow I = P/V