The Resolution was a custom of the Kaelons of Kaelon II when they reached the age of sixty. It consisted of a celebration of that person's life and accomplishments in the company of their family and friends. The person could say goodbye to their loved ones, while still in full possession of their faculties, before undergoing a ritual suicide.
The ritual was proposed between fifteen and twenty centuries before the 24th century in order to avoid societal problems the population faced with their elderly. They were sent to deathwatch facilities where they simply waited for death. Severe overcrowding and detrimental environments led to mistreatment. Furthermore, many families found it hard to visit them when they encountered mental problems. Rather than have families make the decision on an appropriate age for the ritual, an age of sixty was chosen for the ceremony, as a point in life when people could have full possession of their faculties and be able to say goodbye to their families. The ritual became a cornerstone of Kaelon life for the next 1,400 years, and it was taboo to consider not performing the ceremony.
In 2367, Kaelon scientist Timicin requested asylum aboard the USS Enterprise-D while he considered not performing Resolution after learning how close his work had come to saving his planet's dying sun, speculating that it would be easier for him to complete the work himself rather than hand it on to others who may take more time trying to understand his calculations. However, when he was rejected by his people for his attempt to violate the custom, Timicin ultimately returned to the planet and fulfilled his obligation to his family, accompanied by Lwaxana Troi, with whom he had formed a friendship during his time on the ship. (TNG: "Half a Life")