The sun's light (and all light) contains energy. Usually, when light hits an object the energy turns into heat, like the warmth you feel while sitting in the sun. But when light hits certain materials the energy turns into an electrical current instead, which we can then harness for power.
A solar panel (module) is made up a number of solar cells. Solar cells are generally made from thin wafers of silicon, the second most abundant substance on earth, the same substance that makes up sand. To make the wafers, the silicon is heated to extreme temperatures, and chemicals, usually boron and phosphorous, are added. The addition of these chemicals makes the silicon atoms unstable (their electrons less tightly held).
When photons of sunlight hit a solar panel, some are absorbed into the solar cells, where their energy knocks loose some of the modified silicon's electrons. These loose electrons are forced by electric fields in the PV panel to flow along wires that have been placed within the cells. This flow of electrons through the wires is electricity, and will provide power for whatever load we attach (a calculator, a light bulb, a satellite, etc.)
Because solar cells are modular, a system's size can be increased (or decreased) over time, according to need.