How it works
The photoelectric effect is when photons knock electrons off of atoms. Einstein received his Nobel Prize for describing this phenomenon which is at the heart of the operation of a solar panel. The simple explanation of solar power is that energy from light knocks electrons out of place in the solar panels, which then flow through your house, providing electricity.
Before getting into anything more complicated than that it should be clear that the operation of a solar power system is incredibly simple as there is essentially no operation at all. A solar array will silently and reliably provide power to your house and you will absolutely not notice any difference. As far as maintenance goes, a well installed system should require nothing from the owner other than keep the panels relatively clean and free of debris or shading.
Ok, now on to the science. Solar panels that provide electricity are called Photovoltaic (PV) panels. Conventional PV panels are made from silicon, wires, and the framing. Conductors, such as wires, have some electrons which aren't very strongly attached to the atoms and they move around from atom to atom fairly easily. Insulators, such as plastic, don't have loose electrons and they are used to cover wires to protect people from getting shocked.
Silicon is a semi-conductor. In its pure form it is not a good conductor at all but its atomic structure is such that by adding a tiny bit of an impurity you can make it a conductor. In fact, pure silicon has about 30,000 times more resistance than it does when you add amounts of impurities as small as a few parts per million. When you add a tiny bit of phosphorous to the silicon you get a material that has some loosely attached electrons. These electrons aren't exactly extra, but this material is called "N-type" silicon for having extra electrons which, by convention, have a negative charge. If you add a tiny amount of boron to silicon you get a material which has space for extra electrons. These spaces allow electrons to flow through the material and because of the 'lack' of electrons, which are negatively charged, this material is call "P-type" silicon for positive.