According to Reference.com, the function of the round window, a membrane-covered opening between the middle ear and the cochlea, is to allow for pressure changes between the middle ear and the cochlea. The membrane over the round window is called the secondary tympanic membrane. Another term for the round window is the fenestra of cochlea.
HowStuffWorks states that hearing takes place when sound waves strike the eardrum that separates the outer ear and the middle ear. The sound waves are amplified as they travel through the bones of the inner ear. The last bone vibrates against the oval window that connects to the cochlea, a series of fluid-filled chambers arranged in a spiral pattern. The fluid in the cochlea vibrates in response to the oval window, transferring the waves to a system of fibers in the inner ear. These fibers transfer the waves in specific patterns to the organ of corti, which translates the sound waves into electrical impulses, which travel along the cochlear nerve to the brain. The brain then interprets the signals as sounds.
According to HowStuffWorks, the round window is important in this process because the fluid in the cochlea cannot be compressed. When the bone vibrates against the fluid in the cochlea at the oval window, the round window vibrates in the opposite direction to give the fluid room to move and transfer the sound waves.