Psionic energy is generally associated with various mental processes such as Telepathy.
Species with psionic abilities included Betazoids who were able to telepathically communicate within their own species with relative ease. A non-corporeal being known as Onaya had psionic abilities (DS9: "The Muse"). Vulcan mind melds were a form of touch telepathy (TOS: "Dagger of the Mind").
Calafans had psionic abilities, but only in conjunction with their dream states (In Between Days: Reversal, Temper). Dreams could be amplified using a naturally-occurring substance known as callidium, which was present in the extremity skin of full-blooded Calafans and known as calloo (In Between Days: Fortune).