In simple terms, the Bernoulli effect states that if the velocity of a flowing fluid is increased, its pressure must decrease. There are many complicated forms of the Bernoulli equation to relate to different fluids in different situations, however, the main idea is simply a statement of the conservation of energy.
A great way to understand the Bernoulli effect is to think of water flowing down a river. When the riverbed is shallow and narrow, the water begins to flow very fast. When the riverbed opens up to a wide area or is very deep, the water slows down considerably. Fluids behave according to the Bernoulli principle because pressure, velocity and potential energy are all related to each other, and their sum equals a constant. For example, if pressure is 10, velocity is 10 and potential energy is 10, the equation would look as follows: 10 + 10 + 10 = 30. If the velocity rises to 20, there would have to be a decrease in pressure and potential energy for the equation to remain equal to 30 (e.g., 5 + 20 + 5 = 30). This very simply shows that when the velocity of the fluid increases, the pressure decreases.