Solar panels are devices that convert light into electricity. They are called "solar" panels because most of the time, the most powerful source of light available is the Sun, called Sol by astronomers. Some scientists call them photovoltaics which means, basically, "light-electricity."
A solar panel is a collection of solar cells. Lots of small solar cells spread over a large area can work together to provide enough power to be useful. The more light that hits a cell, the more electricity it produces.
Solar panels are made up of photovoltaic (PV) cells, and these cells are made up of materials called semiconductors. During the day solar cells absorb particles of sunlight and convert it into direct current (DC) electricity.
DC electricity travels to a device called the inverter where it converts into alternating current (AC) electricity, the conventional electricity used to power your appliances and home. The inverter is typically installed on an exterior wall or in the garage.
AC electricity then travels from the inverter to your electrical panel (also called the breaker box) and then into your home to power your lights and appliances. Your utility meter measures the energy you use, and when your solar system produces more power than you need this meter spins backwards. Excess energy is fed back to your utility company's grid, earning you credits for contributing to the local energy supplier/Electric Company(you may sell to them).
Most utility meters are digital now, which is way less fun to watch, but don't worry –the savings remain the same.
You're still connected to the grid since you'll need power from the utility company at night. But that's where those credits you earned come in handy: the cost of any power you use when it's dark out will be offset by the clean energy you put into the grid during the day.