"We wish to confirm once more that the task of evangelizing all people constitutes the essential mission of the Church." It is a task and mission which the vast and profound changes of present-day society make all the more urgent. Evangelizing is in fact the grace and vocation proper to the Church, her deepest identity. She exists in order to evangelize, that is to say, in order to preach and teach, to be the channel of the gift of grace, to reconcile sinners with God, and to perpetuate Christ's sacrifice in the Mass, which is the memorial of His death and glorious resurrection. -- Pope St. Paul VI, Evangelii Nuntiandi ("Evangelization in the Modern World")
Put simply, evangelization is the proclamation of the Gospel to the world. This is accomplished through words – that is, explicit preaching of the Gospel message – and through the witness of the faithful through the Works of Mercy and the pursuit of holiness.
All the baptized are called to the mission of evangelization, although how they fulfill that calling will depend on the specific vocation and gifts of the individual. For most Catholics, evangelization will be most evident in how we live together in our communities, extending the mercy and love of God to those around us while being ready to explain how the faith has helped us.
Examples of evangelization include: