Introduction

The word "limbo" comes from the Latin word limbus which means a border, a hem, or fringe around the edge of a garment.

The term is associated in common parlance to mean some in-between state of being. It is often associated, in a religious context, with some state of being in neither heaven nor hell, therefore on the fringe of either. It has been used to refer to the abode for the dead who were neither capable of committing deadly sin (1 John 5:16) which excluded the soul from hell nor were baptized in water and the Holy Spirit (John 3:5) which excluded the soul from heaven.

Catholic Teaching?

There never has been nor is there any official Catholic doctrinal position or teaching on the existence of or state of limbo.

Limbo is not, and never has been, a dogma of Catholic belief, but merely a popular theolegoumenon (theological opinion).

It must be stated that the term limbo receives a lot of attention in pastoral practice when pastors had to explain the mind of God to distraught parents whose newborn infant has died without being baptized.

Catechism of the Catholic Church, Section 1261

As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them," allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.

References

1 John 5:16
He that knoweth his brother to sin a sin which is not to death, let him ask: and life shall be given to him who sinneth not to death. There is a sin unto death. For that I say not that any man ask.

John 3:5
Jesus answered: Amen, amen, I say to thee, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God.