(covers information from several alternate timelines)
The ear is part of a sensory system found in most carbon-based lifeforms, typically, but not always, consisting of a fleshy outer appendage usually called the outer ear, as well as a group of canals and vibration-sensitive membranes and small bones located inside the skull. Ears function by receiving vibrations in the ambient atmosphere and translating them into electrical impulses sent to the brain, which allows a humanoid to 'hear' sounds around them.
Most humanoid species' ears are located on or around the outer areas of the skull, and the sensitivity and range of sounds audible varies greatly among species. The three bones of the middle ear are the malleus, incus and stapes. The ear also has a tympanic membrane which is the connective tissue between the middle and external auditory canal. (VOY: "Eye of the Needle")
Human ears are typically mostly round, fleshy appendages, while Vulcan ears are more typically pointed at the top. These features made Vulcans the frequent subjects of ridicule by Humans, although the stoic Vulcans were confounded by Human "fascination" with their ears.
The Ferengi have large, rounded ears, the rims of which they refer to as "lobes". Physically, the lobes are a highly sensitive area that produce feelings of pleasure and contentment when stroked, as in the technique called oo-mox. However, the lobes are also very sensitive to pain. (DS9: "Family Business") In 2369, while under the influence of the Saltah'na energy spheres, Major Kira Nerys proposed Constable Odo to support her in her "mutiny". If he would do so, she offered him full power on how to handle the martial law on the promenade and even to toss Quark out of the station - on his ears. (DS9: "Dramatis Personae")
In late 2369, Vedek Bareil Antos told Commander Benjamin Sisko that he knew a monk when he was five years old who could "squeeze the pagh right out of your ear with his thumb and forefinger". (DS9: "In the Hands of the Prophets")
Many species, such as the Gorn have no external appendage or visible 'ear' but can hear as well as, and in some cases far better than, species with external auditory organs. (ENT: "In a Mirror, Darkly, Part II")
The sensitivity and hearing ranges for species vary widely, even on the same planet. Vulcan hearing is known to be more acute than that of most Humans. Ferengi have extremely sensitive hearing, as well. Vorta were genetically engineered with no aesthetic sense, but acute hearing, as Weyoun was able to hear Gul Dukat's quiet discussion about his daughter with his subordinate Damar. (DS9: "Favor the Bold")
In 2258 of the alternate reality, while attempting to change her assignment from the USS Farragut to the USS Enterprise, Nyota Uhura reminded Spock of her "exceptional aural sensitivity", a fact which the latter did not dispute. (Star Trek)
The state of being unable to hear, whether by genetic makeup, congenital defect, or external damage to a being's hearing is known as deafness. Some societies consider deafness a weakness or handicap, while others have no social stigma attached to it. (TNG: "Loud As A Whisper")