The LDS Church does not have infant baptism but uses the age of eight as the appropriate age for a child to be baptized because that is the age that they are capable of understanding. It is referred to as the 'age of accountability.' Children are fully capable at this age to understand discernment...also known as the 'Age of reason.' The exact number of eight is due to a revelation given to Joseph Smith in 1831, part of which says, "And their children shall be baptized for the remission of their sins when eight years old, and receive the laying on of the hands." (Doctrine and Covenants 68:27)
There are several other scriptural references explaining that little children cannot receive baptism until they have reached an age when they understand right from wrong. Before this, they are innocent because they do not understand. These verses include Moroni 8:5-26 in the Book of Mormon and Doctrine and Covenants 29:47 and 137:10.
Age of reason (canon law)
In the Roman Catholic Church, the age of reason, also called the age of discretion, is the age at which children become capable of moral responsibility. On completion of the seventh year a minor is presumed to have the use of reason (canon 97 §2 of the Code of Canon Law), but mental retardation or insanity could prevent some individuals from ever reaching it. Children under the age of reason and the mentally handicapped are sometimes called "innocents" because of their inability to commit sins: even if their actions are objectively sinful, they sometimes lack capacity for subjective guilt.
While in the Eastern Churches, Confirmation (also known as Chrismation) and Eucharist are bestowed on the infant who has just been baptized, in Latin Rite Catholicism, confirmation (except in danger of death) may be lawfully conferred only on a person who has the use of reason (canon 889 §2), and Holy Communion may be administered to children only if "they have sufficient knowledge and (are) accurately prepared, so that according to their capacity they understand what the mystery of Christ means, and are able to receive the Body of the Lord with love, faith and devotion. The blessed Eucharist may, however, be administered to children in danger of death if they can distinguish the Body of Christ from ordinary food and receive communion with reverence" (canon 913).
This picture is of the octagonal Baptismal Font at Pisa.
The font itself is of a design stretching back to earliest times--the octagon. Baptismal fonts of octagon form are found all over the world, their eight-sided shape symbolizing regeneration and rebirth. No one is sure just how this custom began, but it is exceptionally ancient. One possible explanation is that the number eight represented one more than the "perfect"number seven, and therefore represented beginning over. Recall that God created the earth in six days and then on the seventh, "He rested." The "eighth" day would be the beginning over or the start of a new week.
The eight-sided shape of these types of fonts could also be symbolic of the age of accountability.