What does it mean when people refer to someone coming into "full communion" with the Church?

It's part of what the RCIA program.  (Rite of Christian Initiation of Adults)  Coming into full communion with the Catholic Church describes the process for entrance into the Catholic Church for people who are baptized Christians but not as Roman Catholics. To become a Roman Catholic, these people, called "candidates," usually participate in a formation program where they learn about what it means to be Catholic.  They are given information to help them understand and experience the teachings and practices of the Catholic Church.  Should they determine that they want to become a Catholic, they make a profession of faith.  They are not baptized again. (The Catholic Church recognizes all mainstream Christian Baptisms.)  This celebrations and coming into "full communion" usually happens at the Easter Vigil ceremony.