The idea of canonising saints is part of the Catholic tradition, though the process was not codified until the 11th Century. Before then a saint was just a locally venerated holy man or woman. To become one now the recipient must be canonised - or bestowed with the title of saint - by the Vatican and the Pope. During the canonisation process a Devil's Advocate contradicts the evidence of any miracles supposed to have been attributed to the would-be saint. Christopher Hitchens famously assumed this role during the canonisation of Mother Teresa. Most modern miracles revolve around "healings" and in the case of Mother Teresa, the claim was that the tumour of a woman undergoing cancer treatment for a year had shrunk - all whilst wearing a portrait of Mother Teresa. Her doctor and her husband say that it was the medical intervention that saved her life whereas for the faithful it was divine intervention by the dead nun.
The list of saints is extensive. For Catholics the saint is akin to a demigod, or someone who has the ability to intervene on their behalf with God and can be contacted through prayer. It helps if there is some sort of object associated with the saint when they were alive - or even body part - close by. Many saints have become patrons of places, groups, activities, jobs etc through tradition. These concepts are similar to the Roman pantheon of gods and these similarities give some indication where the concept may have arisen.
In order to be baptised into Catholicism parents usually bestow a saint's name on the child though this is not mandatory. If the child is later confirmed into the Church the child assumes another saint's name. The commitment to saints is a major defining difference between Catholicism and Protestantism. The latter viewed saint worship as idolatry and eradicated it from their practice of Christianity, though Anglicans keep the saints created before the split from Rome in the 16th Century.