Absolution was the forgiveness of sins in such a way that the one being forgiven no longer held any guilt, or the clearing of one accused of a crime.
According to Q, humans were "all sopping over with compassion and forgiveness. They can't wait to absolve almost any offence. It's an inherent weakness in the breed." After Q confessed that he would not have saved Data the way the android saved him, and that he felt shame at this admission, Jean-Luc Picard told him that he was not the Q's father confessor and would get no absolution from him. This was because of Q's past torment of the crew, which Picard felt might still be happening. (TNG: "Deja Q")
In 2367, Picard agreed to grant political asylum to Ambassador Kell aboard the USS Enterprise-D once he had been absolved of the crime of working with the Romulans to make Geordi La Forge murder Vagh. (TNG: "The Mind's Eye")
In 2372, Tuvok absolved the crew of USS Voyager of guilt, laying it all on himself when he disobeyed orders to contact the Vidiians. (VOY: "Resolutions")