Gyroscopic motion is the tendency of a rotating object to maintain the orientation of its rotation. A rotating object possesses angular momentum and this momentum must be conserved. The object will resist any change in its axis of rotation, as a change in orientation will result in a change in angular momentum. This idea is most obvious when playing with a top. The faster the top spins the more likely it is to stay upright, and it will wobble while it spins. The Earth also has gyroscopic motion (and has wobbles leading to Milankovitch cycles. This same physics is part of why bicycles stay upright (and why people need to lean to turn a bicycle, see hyperphysics).
Gyroscopic motion is used in inertial navigation systems with airplanes and space ships. Gyroscopic motion can create problems with flywheels. Additionally, gyroscopic motion can cause catastrophic failure in wind turbines. This comes from the tendency for a spinning object to want to keep spinning in the same direction.
Below is a video from Veritasium explaining the unique phenomenon of gyroscopic motion and precession. It contains an interesting demo using a spinning bicycle wheel:
You can learn more about gyroscopic motion here.