Solar panels use the photoelectric effect, where a photon of light punts an electron from one material into another. Layers of the right materials are stacked up to create the panel.
With continued light exposure, a steady stream of electrons is pumped from one layer to the other, and this steady stream of electrons is electricity.
Photons carry a bit of energy. The solar panels are semiconductors made in such a way, that if an electron gets a bit of a kick from a photon, it will then escape and travel through a wire as electricity in the desired direction.
The specifics of how exactly that operates is more difficult, because it requires a lengthy explanation of how conductivity works in the first place.
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