What is Catharsis?

Catharsis (Pronounce it  -  from the Greek κάθαρσις katharsis meaning "purification" or "cleansing") is the purification and purgation of emotions—especially pity and fear—through art or any extreme change in emotion that results in renewal and restoration. (Wiki)

Calvet's catharsis: 

how painting saved this colourful artist's life

"Having lived an eventful life as a bent cop, underworld bodyguard, criminal fugitive, nightclub impresario and out-of-control drug addict, Calvet eventually hit rock bottom. He holed up alone for three months in his Nicaraguan villa with nothing but drugs (heroine, crack, alcohol, you name it) and paranoid delusions for company. But just when death was on the doorstep, a remarkable thing happened: Calvet discovered painting. Literally discovered it – in the form of some paint cans under the stairs, which he began cathartically flinging at the walls. 'All my hate came out,' he says. 'It was like I was vomiting non-stop … I saw what was disturbing me inside. In fact, no. I saw what was killing me.'" More here.

As a Literary Term

Catharsis is a metaphor originally used by Aristotle in the Poetics to describe the effects of tragedy on the spectator. 

“Tragedy is an imitation of an action that is serious, complete, and of a certain magnitude; . . . through pity [eleos] and fear [phobos] effecting the proper purgation [catharsis] of these emotions” (c. 350 BCE, Book 6.2).

The Psychoanalytic Use of Catharsis

A catharsis is an emotional release. According to psychoanalytic theory, this emotional release is linked to a need to release unconscious conflicts. For example, experiencing stress over a work-related situation may cause feelings of frustration and tension. Rather than vent these feelings inappropriately, the individual may instead release these feelings in another way, such as through physical activity or another stress relieving activity.

Quotes

The act of writing is a kind of catharsis, a liberation, but I never really concerned myself with that. I write because it interests me. ~Nathalie Sarraute

I thought music could take you to a place where you didn't even feel ownership of it, you just felt lucky you were there. It's like church without God, or something. It's about feeling, hope and catharsis and things that are nurturing.  ~Wesley Schultz

My view of actors is that basically they're all harmless lunatics who'd be on the psychiatrist's couch, except that we get this sort of catharsis every six months or so, and we go and be absolutely someone else.
   ~Michael Caine