The Starnes Exploration party orphans grieving their parents
Grieving or mourning was the natural process of dealing with the loss or death of someone or something.
With grief came a mourning period, or the time that one took following a loss to reflect and come to terms with, so as to readjust to life. According to Julian Bashir, "Klingons usually have a shorter mourning period than Humans. They accept death more readily than we do." (DS9: "Image in the Sand")
The mourning period generally consisted of a grieving process, or a series of emotional stages experienced by the griever, which included: denial, anger, bargaining, depression, and acceptance.
In 2268, much to the confusion of James T. Kirk, Spock, and Doctor Leonard McCoy, the orphan children of the Starnes Exploration Party displayed no signs of grief over the death of their parents, even to the point of continuing to play games in the presence of their corpses. Later, free from Gorgan's influence, they finally broke down and cried. (TOS: "And the Children Shall Lead")
Following the death of Marla Aster, Jean-Luc Picard noted to Counselor Deanna Troi their responsibilities when it came to informing her son, Jeremy, and how it was his was simply to "break the unpleasant news", but Troi was responsible for staying with him "through the entire grieving process." Troi noted that, with her aspect of those responsibilities, "We deal with our pain in many different ways, but over the years I've discovered it is in our joy that the uniqueness of each individual is revealed. If I can help a person back to a state of joy, well, my role has its rewards." (TNG: "The Bonding")