Age of Accountability is the arbitrary age by which a person reaches a level of understanding that ones actions carry a moral consequence.
This term is used by Christian denominations which practice adult (believer's) baptism and reject the doctrine of Original Sin. Young children are seen as being covered by God's grace and not in danger of eternal damnation.
Once a child reaches the point of knowing right and wrong and understands the eternal consequence of sin, the child reaches the age of accountability and is considered to be a candidate for baptism. Some denominations automatically baptize children at a specific age. Others wait for the child themselves to make the decision on when to be baptized.