Clairaudience is the ability to mentally hear what people outside natural hearing range are saying. This is merely an aspect of another psychic ability such as Empathy or Sensing rather than a separate power.
A by-product of channeling heightened emotions is psychically hearing the being(s) they are channeling speak even if they are outside natural hearing range.
This will drive a human being insane if they obtain Empathy but was never destined to have it. They will fight against the emotions and the voices in their head, but it will ultimately kill them unless the power is withdrawn. However, with guidance from a true Empath a human can learn to control the power, turning it on and off at will.
One notable instance of Clairaudience was when Prue Halliwell gained Empathy unnaturally. While she was temporarily an Empath, Prue was able to hear the arguments people were having all over the city. This was due to Prue's Empathy picking up on the intense emotions behind the angry words people were shouting at each other.
While humans can learn to embrace the emotions and the voices connected to them, demons will not be able to. The crushing weight of human emotions and the voices connected to them will drive a demon insane, but not kill them. Vinceres is a prime example of this, he was driven insane but was able to fight the effects to stay alive.
A by-product of reading people's thoughts is psychically hearing the being(s)' thoughts they are channeling speak even if they are outside natural hearing range.
One notable instance of Clairaudience was when Christy Jenkins eavesdropped on the Charmed Ones' conversation from Magic School.
One vital aspect of a Whitelighter's and certain Cupid's power to sense and locate charges is the ability to psychically hear their charges speak, even if they are miles aways. It allows their charges to contact and communicate with them, by first calling their name to draw their attention. However, as proven by Chris Halliwell when he heard Phoebe Halliwell calling for him, charges can be put on mute by Whitelighters.
During one of Piper and Leo's heated arguments, Wyatt used his magic to swap their powers, giving Piper all of Leo's powers, including the power to sense his charges. Using his sensing ability, Piper could hear Phoebe calling out to her for help.