Aristotle Poetics VI. Tragedy . . . is an imitation of an action that is serious, complete, and of a certain magnitude . . . ; through pity and fear effecting the proper purgation [or catharsis] of these emotions [i.e., pity & fear]. . . .also IX. . . . again, tragedy is an imitation . . . of events inspiring fear or pity. Such an effect is best produced when the events come on us by surprise; and the effect is heightened when, at the same time, they follow as cause and effect. . . .
XIII[a]. [A perfect tragedy should] imitate actions which excite pity and fear [catharsis], this being the distinctive mark of tragic imitation.
XIV[a]. . . . the plot ought to be so constructed that, even without the aid of the eye, he who hears the tale told will thrill with horror and melt to pity at what takes place [catharsis]. This is the impression we should receive from hearing the story of Oedipus.
A persistent issue in Aristotle's description is his metaphor of "purging" or "catharsis" to describe the desired effect of Tragedy as an exercise of "pity and fear."
Definition of "catharsis" from Oxford English Dictionary:
etymology: [modern Latin < Greek cleansing, purging . . . ]
a. Purgation of the excrements of the body; esp. evacuation of the bowels.
b. The purification of the emotions by vicarious experience, esp. through the drama (in reference to Aristotle's Poetics 6). Also more widely.
c. Psychotherapy. The process of relieving an abnormal excitement by re-establishing the association of the emotion with the memory or idea of the event which was the first cause of it, and of eliminating it by abreaction. [Abreaction: Discharge of the emotional energy associated with a psychic trauma that has been forgotten or repressed; the process of bringing such a trauma back to consciousness, esp. as a psychotherapeutic technique . . . .]
possibilities for catharsis
The metaphorical referent for catharsis is repellent to modern audiences but may have been less so to earlier audiences, for whom traditional medicine was often based on cleansing or purging in terms of digestion or even bloodletting.
Fear and pity are not normally associated with aesthetic pleasure. Most people read a book or see a movie to identify with triumphant heroes, to laugh, or to escape (transcend), all of which generate feelings of superiority.
Possible rationalizations of fear and pity as desirable narrative outcomes.
1. Fear and pity as complementary repellent and attractive forces appropriate to tragic art:
The combined attraction-repulsion of fear and pity may be analogous or parallel to the aesthetic sensation of the sublime, which is the most powerful of responses because it mixes beauty (which attracts us to something) with terror or fear (which repels us).
Another formula for the sublime is a mix of pleasure and pain: that to which we are attracted, and that which we avoid, as with "fear and pity."
2. Fear and pity are normal human responses to our own and each other's conditions needing expression and exercise.
We often repress fear and pity—fear for obvious reasons, pity so we can feel superior to or separate from suffering of others. (Pity generates identity, sympathy, empathy, or compassion for others.)
Repression of such impulses is normal but potentially dangerous, building frustration and anxiety.
Vicarious experience—actions or sensations experienced imaginatively through another person or agency (such as art)—may process repressed impulses in a harmless or beneficial way.
Watching or reading a tragic narrative exercises expression of fear and pity, purging or cleansing our backed-up problems and teaching us to manage such feelings or attitudes.
Therefore, even if we have difficulty imagining getting pleasure from a tragic narrative, the vicarious experience of suffering and compassion may make us feel relieved of suffering and more connected to other people.
The development of tragedy may have evolutionary purposes beyond our immediate likes and dislikes.
3. The medicinal metaphor of catharsis, purgation, or cleansing may be appropriate given that problems in Tragedy often appear as disease, blight, sterility, or poison—a force or entity that threatens the health of nature or society.
Oedipus the King where the Priest in the opening scene informs Oedipus:
Disease infects fruit blossoms in our land,
The disease is serious and affects everyone, and the cure is described in ways that are metaphorically consistent, as when Creon returns from the Oracle at Delphi with a message from Apollo, the god of medicine and healing:
Lord Phoebus clearly orders us to drive away
At the end of the tragedy (l. 1697), Oedipus implores Creon, "Cast me out as quickly as you can."
Through catharsis, an audience watching a tragedy implicitly undergoes the same crisis and resolution of disease or uncleanliness and healing or purification.
Shakespeare's Hamlet is described with similar figures, and the character Hamlet reinforces such imagery throughout the play.
Most famously, in Act 1 when Hamlet encounters the ghost of his slain father the old king, the palace guard Marcellus intones:
Something is rotten in the State of
In Act 3, scene 4 when Hamlet challenges his mother Queen Gertrude with his repulsion over her marriage to his father's supposed murderer, he uses imagery such as "mildew," "rank sweat," "enseamed" or greasy, "corruption" and "nasty sty."
Here is your husband, like a mildewed ear, / Blasting his wholesome brother. . . .
Nay, but to live / In the rank sweat of an enseamed [greasy] bed, / Stewed in corruption, honeying and making love / Over the nasty sty! [sty = pig pen] 
Comparably, in O'Neill's Desire Under the Elms, characters often speak of each other as "poison" or "something unnatural" that must be detected and removed.
Summary: Everyone wants to escape or transcend problems, but problems remain around or inside us, waiting to be dealt with.
Tragedy admits and confronts problems inherent in human nature.
There now, that wasn't easy, but don't you feel better?