As Catholics, we honor the saints, the holy men and women that lived their love of Jesus Christ in unique and extraordinary ways. They are models to us. Their teachings and writings inform us. Their charitable acts inspire us. While we might live in different times, the example of how they lived their lives might help us live ours.
The saints are our 'heroes'. They are the models that we follow. We do not worship them, but we do honor them. First among the Saints is the Blessed Virgin Mary, Mother of our Lord. We honor the apostles and evangelists - the first followers of Christ. The various people of Jesus's day that we recognize as saints remind us that everyone is invited to lives of holiness. The martyrs - those who witnessed to Jesus Christ by their deaths - show us how to live with conviction. Among the other classification of saints are pastors (priests, bishops, and popes), religious, and holy men and women.
While saint refers to any holy person, the Roman Catholic Church recognizes men and women who have died and we believe already share in the the Resurrection of Jesus and enjoy the Beatific Vision of the Holy Trinity in Heaven. Some of those in heaven are formally recognized, either through popular acclaim as were many in the early Church, others through a formal canonization process (See below for more information on that to help know the classification).
The Church's teaching on Saints is perhaps best summed in the Opening Collect of All Saints Day:
Almighty God, you have knit together your elect in one communion and fellowship in the mystical body of your Son Christ our Lord: Give us grace so to follow your blessed saints in all virtuous and godly living, that we may come to those ineffable joys that you have prepared for those who truly love you; through Jesus Christ our Lord, who with you and the Holy Spirit lives and reigns, one God, in glory everlasting. Amen.
Saint of the Day:
The Vatican's Saint of the Day
Collections of Saints biographies
Catholic.org Collection of Saints
My Catholic Life Collection of Saints
AboutCatholic Collection of Saints
CatholicSaints collection of Saints
Roman Catholic Saints Collection of Saints
Collection of US Holy Men and Women
USCCB's American Saints and Blesseds
The Canonization Process
After the person's death, the diocese in which they lived and died might be petitioned to begin the formal process to examine the person's life. It should be noted that the process does not say that the person never sinned or made errors, but rather did appropriate acts of penance and sought reconciliation. All during the process, the Church takes a skeptical eye toward the process, in fact the term "Devil's Advocate" comes from this process and that of confirming miracles (a process that is very much a part of canonization) as a person is appointed to raise all objections toward the person's sanctity or the miracles ascribed. Usually there is a 5 year waiting period between death and the formal petition, unless the Pope waves this period.
As the first step, the local bishop does a preliminary investigation into the person to see if there is readily apparent reasons to open up a case. If there is, he must formally petition the Vatican, in particular the dicastery (the official Church office) of the Congregation of the Cause of the Saints. a complete record of the person's life is collected, and includes not only biographical material, but eye-witness accounts and testimonials. The person's writings are examined for sound teaching (if there was erroneous teaching, the will need to be proof of later evidence of retraction and correction).
If there is ample evidence to continue, the person is named a "Servant of God". The material that was gathered in the local process is ceremonially wrapped and then sent to the Congregation of the Cause of Saints, were members will be selected to read the materials. A postulator for the cause will be appointed, and this person will help keep the process moving forward and aid in communicating to the diocese, the faithful, and others. Again, there is a person appointed whose expressed purpose is to raise objections. If the person is found to be virtuous and heroic in the faith, he or she will receive the title Venerable.
If the person was killed either in defense of the faith, for died because of love of the faith, or killed for hatred of the faith, the Congregation will seek to prove that it was Martyrdom If the person was not martyred, the postulator will seek proof of a miracle that is beyond explanation. This process is formal, and involves scientists and doctors, many of whom may not even believe in the Lord. If there is consensus that the act which is credited to the Venerable person after their death is without any other scientific or medical explanation, they declare a miracle has occurred. After recognition of either martyrdom or a miracle, the Congregation will propose to the Pope that the person be Beatified. Usually this occurs in a formal ceremony at a Mass. (Lately, many Beatifications are occurring in the diocese or country that brought the cause forward. After this formal act, the person is given the title Blessed.
The Postulator again will seek a miracle out, either the first for a martyr or a second for others. Following the same process, the Congregation will recommend canonization of the person to the Pope only after the confirmation of an otherwise unexplained act credited to the person. If the Pope accepts their recommendation, a date is set for a formal declaration, again typically within Mass, in which the person is declared a Saint. Note that they do not 'become' saints, but rather declared to already be in the presence of God.
Typically, the celebration of the blessed or saint is recommended before their beatification. Typically their celebration would be the day they died, but sometimes it might be moved to avoid Lent (when the celebration of Saints is kept to a minimum) or because a more prominent saint might be already celebrated that day. For example, St. John Paul II died on April 2, 2005, a date that is typically in Lent or Easter. His feast is on the anniversary of his election to the Chair of Peter as Pope,