Comets are small bodies made of rock and ice that orbit the Sun.
They orbit in elliptical orbits. While closer to the Sun, comets receive more radiation. This often causes the material on the surface of the comet to heat up and separate from the comet. This gives comets their 'coma' or fuzzy appearance. Sometimes the material of the coma is swept away from the comet by the solar winds and this causes a 'tail' to develop.
This tail is often split between small, light material, such as water vapor and gases, and heavier material such as dust. The light particles will be swept away at higher speeds and tend to form a short lived tain directly away from the Sun. The heavier particles move away at a slower velocity and form an arching tail that follows from the path of the comet.