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.  

I have a question on Matt 10:34 "My mission is to spread, not peace, but division." -Matthew 10:34 We call Jesus the "Prince of Peace" (Is 9:5), so how can He say he won't bring peace?

It is a confusing statement, isn't it? 

Here's the way the Catholic Bishops have explained this:  Jesus, "divides and separates us from all that keeps us from a close, intimate, personal relationship with Him. He wants full communion with us and nothing less. He has come to divide us - to tear us from relationships with people and things that are keeping us from being closer to Him."  So, how can we be in full relationship with the 'Prince of Peace?  First we must examine our relationships. and ask ourselves some questions such as: "Am I spending time with any people who are pulling me away from Christ? Am I  spending too much time in front of the TV or wasting too much time with electronic devices or other inanimate objects that keep me from prayer time?" Are any of my relationships more important to me than my relationship with Jesus?  If the answer to any of those questions are, "Yes," then I need to "cut them out" of my life.

Jesus wants to mean everything to us.   We can let Him into our lives today in a bigger, more profound way:  We just have to "make the cut."

One Bread, One Body   Monday, July 14, 2014   http://www.usccb.org/bible/readings/071414.cfm

If we went high enough into the sky, would we run into heaven? - Tina

Tina -
We don't know EXACTLY where heaven is, but we know it's not here in the realm in which we are living right now.  When Jesus ascended into heaven He went up - away from the disciples - on a cloud.  So, we point into the sky - which is away from where we are.  But that doesn't mean it is actually up.  We could never get in a rocket and fly to heaven.  It is a different realm; a different state of being.  We have to change to get there.  But we know it does exist because Jesus told us it does.