Centripetal force creates a moving gap between fabric and a washing machine, which allows clothing to flow freely around the perimeter of the drum. This high-speed motion of spinning makes clothing take on its own motion within the drum. Excess water is thrown out of the fabric and propelled into the drain as the water moves through the clothes and into the gaps in the drum.
Centripetal force pushes objects away from the center of a circle. Just as a race car driver is propelled to the far edges of a circular track while in motion, clothing in a washing machine is pushed to the edge of the barrel because the force of motion repels the center of the machine. Water is thrown out of the fabric at high-speeds as this force of motion propels out of the fabric.
According to Explain That Stuff, centripetal force is what makes them spin in a circle; this force prevents water from slipping through the drum holes. While the clothes actually experience centripetal force, and the water doesn't; this reaction actually occurs due to the fact that the clothes are spin. This process is often referred to as the spin cycle, which is used to squeeze water out of the clothing.