Bernoulli's principle can be derived from the principle of conservation of energy.
This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline.
This requires that the sum of kinetic energy and potential energy remain constant.
Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy.
In the above diagram, where the air is moving fast, it's static pressure is low.
In the above diagram, consider the blue-shaded area to be the profile of an airplane's wing - a "half venturi".
The wing can lift the airplane because the air pressure above the wing is lower than the air pressure below the wing.