I am so sorry if I am missing something, but for some reason I am very confused on how water can have pressure but not be compressible. If pressure is created by individual molecules bumping into the container, how is this any different than temperature? And how can a water compressor, (an offset wheel inside a container) pressurize water? How is a cup of water under 10 bars of pressure any different than one under 1 bar at the microscopic level. Thank you so much for your input.
It can be compressed, due to extreme pressure, but only slightly. The Wikipedia page on the Mariana Trench says that the seawater density is 4.96% greater there than at the surface.
Also refer to Hydrostatic pressure - doesn't density vary with depth?.
Further explanation (and assuming everything you currently know about water is that it isn't compressible):
You're likely conflating pressure and density. These are two different physical properties. Compressibility implies increasing density, not (necessarily) pressure. You can change the density of a gas without changing its pressure by decreasing its volume and temperature simultaneously. (Think ideal gas law.)
Changing water pressure implies something is applying a force to the enclosed body of water. For the example of water pressure at the bottom of the oceans, the force is Earth's gravity, and the "enclosure" is the surface of the Earth (which may seem counter-intuitive, given how the surface "opens up" to outer space, but remember that gravity is keeping the water pulled towards the Earth). Note that, at the bottom of the trench, gravity is also pulling all the water above it downwards, thus explaining why the pressure is so high in the trench (15,500 psi or 106.9 MPa).
Please note that the density of Water can be modified by its temperature (in which case the water is behaving similarly to an ideal gas, but only in this context) and salinity (in which case its chemical composition is changing).
(Going on a tangent: Sugary Coca-Cola™ is more dense than Diet Coke.)
Also note that I'm intentionally using Newtonian gravity (instead of GR) as part of the KISS method.
EDIT: Changed psi value to more accurate value.
EDIT 2: The Department of Redundancy Department™ corrected "more dense per unit volume". How embarrassing! ;-)