In the Catholic Church, "Venerable" is a title given to a deceased person who, having already been declared a "Servant of God," is recognized as having lived heroic virtues. This is the second step in the four-step process towards canonization, or being officially recognized as a saint by the Church.
After the investigation into the person's life, teachings, and works initiated during the "Servant of God" stage, the Congregation for the Causes of Saints can recommend to the Pope that he proclaim the person's heroic virtues. The Pope, if he agrees, can then make a formal declaration that the person lived a life of heroic virtue. This person is then referred to as "Venerable", and the faithful are encouraged to ask for their intercession.
Being declared 'Venerable' is the second of the four stage process of being declared a saint by the Catholic Church.