Hearing, also known as the auditory sense, was the ability to sense sound with one's ears.
Elderly humans could sometimes develop difficulty hearing, but with proper medical treatment, this was preventable. (TOS: "The Deadly Years", VOY: "Endgame")
In his poem "Ode to Spot", Data observed that Spot's auditory sense, along with his visual sense and his olfactory sense, contributed to his hunting skills and natural defenses. (TNG: "Schisms")
When Julian Bashir heard a sound within his comatose hallucination but Elim Garak could not, the latter speculated that humans had better hearing than Cardassians. (DS9: "Distant Voices")
When three elderly Drayans noticed that Tuvok had pointed ears, Elani asked him if they improved his hearing. He responded in the negative. (VOY: "Innocence")
Deafness was the lack of a sense of hearing.
Ferengi, due to their large ears, had a very acute sense of hearing, and thus could find loud sounds irritating. (DS9: "Crossfire", "Profit and Lace")