A gyroscope is a device that spins around which is actually mounted on an axil in such a way that it is free to move about in a direction which can alter. It spins on an axis. When the mounting tilts, the direction it is spinning in is not affected. That makes it very useful for use in navigation and for giving directions because of its correlation to gravity. It is helpful to pilots and others of the like. The torque plays a big part of the set up as well.
The rotation of the two perpendicular axes that are perpendicular is a result of the applied torque in relationship to the other one when the wheel is spinning. The whole apparatus produces opposition which depends upon the momentum of the angle it is spinning in for the direction it spins in. It is a fairly simple device that offers a world of help when determining direction and navigation.