Comets are basically dusty snowballs which orbit the Sun. They are made of ices, such as water, carbon dioxide, ammonia and methane, mixed with dust. These materials came from the time when the Solar System was formed. Comets have an icy center (nucleus) surrounded by a large cloud of gas and dust (called the coma).
Comets go around the Sun in a highly elliptical orbit. They can spend hundreds and thousands of years out in the depths of the solar system before they return to Sun at their perihelion. Like all orbiting bodies, comets follow Kepler's Laws - the closer they are to the Sun, the faster they move.