Hydrostatic pressure and air pressure

You can clarify the fact, that the hydrostatic pressure increases with depth of immersion with the following experiment:
A rubber balloon is fixed onto a long glass tube. Now the balloon is filled with dyed water (you can use watercolours for example) and is immersed in a deep pot filled with water (see picture below).

You can observe that the balloon is compressed more strongly while being immersed more deeply and thereby the water in the glass tube rises higher. Thus the pressure rises with increasing depth of immersion.
While emerging, the process is reversed: The water from the tube can flow back into the balloon, because the balloon is decreasingly compressed while emerging.

The picture shows that the balloon is being compressed strongly, if it is deep in the water.

This principle is used in pressure measuring devices.