The age of reason is the term most often used to describe when a person becomes morally responsible. It is generally considered to be age seven, although some people may reach it at an earlier or later age, or in cases of severe special needs, maybe not at all.
The Church uses this as a guide for the religious participation of children in the Sacraments and other aspects of Catholic life. Children under the age of seven are not bound by ecclesiastical laws, for example. So if a child who has not reached the age of reason missed Mass on Sunday or a holy day, it would not be a sin. They are also exempt from Lenten disciplines like abstaining from meat on Fridays.
In 1910, Pope St. Pius X issued the decree Quam Singulari, which said that children reached the age of reason around the age of seven, with discretion being left to the family and priest. Currently this is when most children make their first Confession and First Holy Communion, although there are exceptions that allow a child to receive earlier, particularly if that child is in danger of death, understands Who the Eucharist is, and can receive reverently. This is also the age at which children can first lawfully receive Confirmation. There are several dioceses within the United States that have started to permit or even promote this earlier reception of Confirmation. The Eastern rites of the Catholic Church are allowed to administer the Sacraments to children at any age.
One of the important duties of parents is to make sure their children are prepared to receive these Sacraments when they reach the age of reason. There are great tools out there to help parents with this task. Below are just a few of the books and videos available. Check out also the Jesus Our Life text and activity books for more formal instruction.