The cork moves (oscillates) up and down between crest and trough, with the mean position being the water level before the disturbance was created.
The motion is a simple harmonic motion in vertical direction. It is periodic, perhaps the displacement of the cork varying as a sine function.
These are called mechanical waves. The energy propagates from the point of disturbance radially outward to the bank of the water pond.. Since the oscillations of particles are perpendicular to the propagation of the wave, it is a transverse wave.
The same kind of wave is not possible with mechanical waves in air or gases. The molecules of air are very far away from each other. Density is low. There is no force that ties the molecules together like in water or in a solid. So transmission of wave perpendicular to the vibration is not possible.
In air there are pressure waves , in which particles oscillate in the same direction as the propagation of sound/pressure waves.