Earth’s moon is relatively large. This is unique for large planets in our solar system. Mercury and Venus have no moons, and Mars has only two small asteroid-sized objects (Phobos and Deimos) orbiting it. Uranus has 27 known moons. Neptune has 13 known moons. Neptune’s moon Triton is as big as the dwarf planet Pluto. Pluto’s large moon Charon is about half the size of Pluto but Pluto is no longer considered a planet. Saturn has 53 known moons (plus 9 awaiting official confirmation). Jupiter has 50 known moons (plus 17 awaiting official confirmation), including the largest moon in the solar system, Ganymede.  But, the ratio of Ganymede’s mass to Jupiter’s mass is far less than ratio of our moon’s mass to Earth’s mass.
The other planets in the solar system used gravity to capture free floating bodies. But, Earth’s moon was created when a Mars-sized body slammed into the young planet . The Earth formed 4.56 billion years ago, and the Moon formed about 30 million years later. 
The unique mass ratio and the distance between the Earth and the moon creates such a system that resembles an ice-skater with horizontally extended arms. In the Earth-moon system the moon is the extended arm which makes the spinning of Earth more stable. Without the moon’s stabilizing effect, astronomers have predicted that Earth’s tilt could vary as much as 85 degrees.
The axial tilt of Earth oscillates between 22.2 and 24.5 degrees with a period of 41 thousand years. The axial tilt angle is currently decreasing. This is the main wobble of the precessional rotation. There are other wobbles such as the Chandler and Markowitz wobbles.
The cause of the wobbles is the bulging of the Earth near the equator. The bulging was originally formed because of Earth’s rotation around its axis. The Sun, the Moon and the other planets exert a pull on the Equatorial bulge trying to align the equatorial plane with the Ecliptic plane. Angular momentum created by Earth’s rotation around its axis and Earth’s revolution around the sun resists these pulls. The result is a complicated motion of the spin axis in space.
Moon spins around it’s axis in 27.3 days (sidereal period) and completes a revolution around the Earth with respect to fixed stars in 27.3 days as well. These periods are equal. This is why we always see the same side of the moon from Earth. The synodic period of the Moon is longer than the sidereal period. Since the Earth is moving in its orbit around the Sun while the Moon is rotating around the Earth it takes the moon little more time to show the same phase of the light towards Earth, which is about 29.5 days (synodic period).
Moon is slowly moving away from us due to tidal effects. The same mechanism is also slowing down the Earth’s spinning rate. In the far future the gravitational attraction between the moon and the Earth will be less and the Earth’s axis will wobble more.