The word saint literally means “holy,” and, in the New Testament, saint referred to all who believed in Jesus Christ and followed his teachings.
Saint Paul often addressed his epistles to “the saints” of a particular city (see, for instance, Ephesians 1:1 and 2 Corinthians 1:1), and the Acts of the Apostles talks about Saint Peter going to visit the saints in Lydda (Acts 9:32). The assumption was that those who followed Christ had been so transformed that they were now different from other men and women and, thus, should be considered holy.
Canonized and Acclaimed Saints
Most of the saints whom we refer to by that title (for instance, St. Elizabeth Ann Seton) have gone through this process of canonization. Others, such as Saint Peter and Saint Paul, received the title through acclamation, or the universal recognition of their holiness.
Catholics believe that both types of saints (canonized and acclaimed) are already in Heaven, which is why one of the requirements for the canonization process is proof of miracles performed by the possible saint after his death.
Canonized saints can be venerated anywhere and prayed to publicly, and their lives are held up to Christians still struggling here on earth as examples to be imitated.