Mitigation is the act of lessening or easing the harshness of a punishment, a fine, or someone's pain. In the legal world, a lawyer might ask a judge for mitigation of a particularly harsh sentence.
Mitigation is the noun form of the verb mitigate, which means "to lessen in severity." After a natural disaster, the government might offer mitigation, in the form of aid, to ease people’s suffering. If someone tries to make an offense seem less serious by offering an excuse, that's also mitigation. If you miss your curfew, you might state in mitigation that you came home late because you were helping an old lady cross the street.