Why is torture done?

Authorities have two main purposes for torture, either information or punishment.  Some scholars of torture and law codes (such as the UN Convention) leave out the punishment side of torture.

Intimidation and cruelty might be two more possible motives for torture.  Intimidation would seek to discourage people from certain behaviors or beliefs through the fear that they also might be tortured.  Some authorities might simply enjoy inflicting pain on others. Civilized people would probably claim to avoid such uses of torture, although it seems human nature easily slips into the torturer mentality (see the Stanford Prison Experiment). 
Authorities might also conceivably use torture for behavior modification, as per fictional accounts such as A Clockwork Orange or 1984.  Such methods, however, could be properly included under the punishment (and rehabilitation) aspects of torture. 

Information

The easiest way to obtain a conviction for a crime is by confession of the accused. Pressure to obtain such a confession can easily lead to abuses, including outright torture.

Even where torture is officially and legally prohibited, the legal concept of the idea of a crimen exemptum or an exceptional crime or emergency allows for exemptions from legal procedure, ranging from violating rules of evidence to applying torture.  In the Witch Hunts, the fear of magic and its power often allowed authorities to excuse themselves from strict observance of legalities. 

Another excuse for allowing torture is the ticking time bomb myth or the idea that some disaster may occur if someone isn't tortured into telling the truth soon enough.  Lawyer Alan Dershowitz has made many arguments for allowing, but regulating torture in such situations. Such emergencies with knowing perpetrators under a tight deadline, however, are drawn almost entirely from fiction, not the real world. 

Punishment

Convicted criminals might be pardoned or granted mercy, but throughout civilization, they have often faced harsh punishments for even minor offenses.

The Eighth Amendment to the United States Constitution prohibits inflicting "cruel and unusual punishments." People argue about what those are, especially since many punishments which were once clearly cruel are no longer usual in advanced industrial Western societies. Among those societies, capital punishment, or the death penalty, is part of this disagreement, with only the United States still executing convicts.

For more on "What are the methods of torture" used by legal authorities, whether for information or punishment, click here.