The term guardian angels refers to the belief that each soul has an angel available to guide the soul through life and helps us find God.
The belief in the reality of angels, messengers of God and the interaction with them goes back to the earliest times. A Cherubim kept Adam and Eve in Eden. Angels saved Lot(Gn. 19,15) and helped to destroy the cities of the plains. In Exodus Moses follows(Ex. 14,19) an angel and at some point, an angel is appointed “leader” of Israel. The archangel Michael is at various points, Rafael appears in the life of Tobias (the whole book) and Mary receives the visit from Gabriel delivering the Annunciation of Christ’s coming.
The concept of a soul having it’s own guardian angel is also very old and long accepted by the Church.
In Matthew 18,10 Jesus says:
Look, do not despise one of these little ones: for I tell you that their angels in heaven always see the face of my Father which is in heaven.
Several New Testament passages suggest the existence of guardian angels. An angel comforted Jesus in the Garden of Olives, another helped Peter out of prison.