The moon is a natural satellite of the Earth. In general, the term "moon" denotes an object that orbits something other than the star in a solar system. In this respect, the Earth's moon is similar to the moons of Jupiter or any other planet. Moons are not classified by their mass, size or composition. Instead, they are classified by their motion.
Dynamics and Motion
The objects in the solar system are classified foremost by their dynamics and motion. While size and composition are important for secondary classification, the solar system itself is defined by the orbits of its constituent bodies. Classification by motion is more useful for astronomers. In fact, the dynamics of the solar system were a central issue for early astronomers such as Ptolemy in the second century and Nicholaus Copernicus in the 16th. Later, the observations of Galileo and the laws of Johannes Kepler helped anchor human understanding of the solar system around the motion of its bodies.
The moon's composition is very similar to the four terrestrial planets: Mercury, Venus, Earth and Mars. These bodies have rocky surfaces, distinct geological layers and have few or no moons. Because the moon is similar to the terrestrial planets, it is sometimes discussed alongside them. The classification of bodies in the solar system, however, remains primarily based on motion. Hence, the moon is not recognized as an official terrestrial planet or a dwarf planet.
Planets and Moons
Planets in the solar system orbit the sun in a path that is clear of other large objects. The planets are sufficiently massive to keep their orbits even in the face of other gravitational bodies such as asteroids. The gravity of each planet can lead that planet to acquire a number of natural satellites: bodies that orbit the planet but do not interfere with the planet's revolution about the sun. These bodies are called moons.
The Moons of Other Planets
Other planets in the solar system have moons based on the same classification principle as the Earth's satellite. For example, Mars has two small moons that orbit it. Jupiter and Saturn each have at least 50 moons. Additionally, some of the moons that orbit the outer gas giant planets have a similar terrestrial composition as the moon and the inner planets. Given that they orbit around planets, however, they are classified as moons.
The Earth and the Moon
The moon exerts a gravitational pull on the Earth but not enough to disturb its orbit. The gravitational force of the moon does create the tides Earth experiences in large bodies of water. But the Earth is the dominant gravitational body. Given the similarities in size and composition between the Earth and moon, some astronomers theorize that the moon formed after another body collided with the Earth.