What it means to be Blessed.
Up until the beatification of a Servant of God Catholics must observe a strict rule of non cultus, meaning that while they may privately pray to and venerate an individual whom they believe to be in heaven there may not be any public acts of religious veneration. In fact, the presence of a cultus before the approval of the Church is given can end the candidacy of a Servant of God.
With Beatification a number of marks of veneration can be given to a person. The most important one is that a feast day, with its proper Mass and Office (Liturgy of the Hours), can be granted to particular dioceses and religious orders and congregations. For example, Blessed Takeri Tekawitha, the Lily of the Mohawks, is celebrated on the liturgical calendars of the U.S. and Canada. In the U.S. and Mexico there is a feast day for Blessed Juan Diego, the visionary of Guadalupe. By analogy, this privilege is somewhat akin to the practice of episcopal canonization earlier in Church history, except that a bishop manifests to Rome his flock's desire to venerate a Blessed and Rome grants such local veneration.
With beatification comes the restricted right to venerate the relics of Blessed Teresa, to have public prayers to them and to honor their images in places of worship where this is granted by the Holy See. It is restricted in the sense that it is the veneration of a part of the Church and not the whole, and lacks the finality of canonization.