What role does the eardrum and ossicles play in hearing, versus cilia?
Sounds are pressure waves in air, but the inner ear is a liquid-filled space. This presents an impedance matching problem where sound is reflected rather than transmitted.
The eardrum and inner ear bones perform this mechanical impedance matching/transduction of air-to-liquid sound. From Purves' Neuroscience:

Sounds impinging on the external ear are airborne; however, the environment within the inner ear, where the sound-induced vibrations are converted to neural impulses, is aqueous. The major function of the middle ear is to match relatively low-impedance airborne sounds to the higher-impedance fluid of the inner ear. The term “impedance” in this context describes a medium's resistance to movement. Normally, when sound travels from a low-impedance medium like air to a much higher-impedance medium like water, almost all (more than 99.9%) of the acoustical energy is reflected. The middle ear (see Figure 13.3) overcomes this problem and ensures transmission of the sound energy across the air-fluid boundary by boosting the pressure measured at the tympanic membrane almost 200-fold by the time it reaches the inner ear.

Some sources will refer to this as &quot;amplification&quot; which is correct in some ways (without it, sound would be too &quot;weak&quot; in the inner ear) but doesn't quite explain the whole problem.
Inner hair cells do the actual sensory transduction, converting vibrations into electrical signals when the &quot;hairs&quot; are stretched apart mechanically, causing a fragile &quot;tip link&quot; to pull on a physical channel, opening it and allowing ions to flow through. The cochlea is a frequency-analyzer, vibrating at different frequencies along its length and allowing different hair cells to respond maximally to different frequencies of sound.

As a side note, although you asked about vertebrates, aquatic vertebrates like fish don't have these middle ear bones, their hearing is quite different from the mammalian ears I am most familiar with. I'm not sure at all about hearing mechanisms in aquatic mammals that evolved from terrestrial ancestors, like whales and dolphins, but that might be a good subject of a later question.