The word 'covering' is not new around the church. We have all heard references to spiritual covering, like: - "Who is your spiritual covering?", "What is your spiritual covering?", or "You should be under covering," etc.
Generally this expressed the need for everyone to be a member of a church. The pastor of that church (or the church itself) was seen as your spiritual covering. To say you were ‘under covering’ meant that you ‘belonged’ somewhere in the Body of Christ, and by belonging to a specific church this provided you with your bona fides as a Christian. This meant you were not independent, you were submitted and accountable, you had a shepherd (someone who watched over your soul, someone who could presumably correct you if you were deceived or went wrong) and because of that you would be seen as a genuine Christian. Thus you were seen as being "under covering."
Covering is a Great Deal More Than That
Covering is in fact more that this, and occupies another dimension entirely. Under true covering, spiritual power is flowing and is at work because something appointed by Christ is in place. A spiritual covering is a spiritual force field which helps bring in good things (blessings) and keep out bad things (protection). The life and power is provided by those anointings of Christ that flow through apostles, directly or indirectly.
The covering of Christ is vested in certain men (i.e. specific individuals). God has always done things this way and there are many Scriptural examples. Adam was a covering for the entire human race and when he fell, we all fell. Abraham was a covering to us and because of his standing as the Father of Faith, we are children of Abraham and we inherit blessing because of him. Paul is the Apostle to the Gentiles and a Father to us all. We have inherited much good and blessing because of Paul. The Bible has many examples of men whose lives were a covering to others and through them God was able to bless and protect His people.
If we would have the full measure of the blessing of Christ, we need to have in place the relationships appointed by Christ that are a covering for us. By this we see that our lives are affected by other people. Our lives are impacted by those who are over us in the Lord whether we like this concept or not.
In churches where there is an anointed leader and unity amongst the supporting leadership, there is always a certain level of covering and protection. This kind of leadership which seeks to follow Christ and work together always provides a good place for people to grow in Christ, to serve, to be blessed and to find what God has planned.
However there is a level of covering that is even above this - an apostolic covering. When we are in proper relationship directly or indirectly with the apostle's that God has placed over us, we find that this brings covering, blessing, protection, and a spiritual dynamic of good that we may not even understand. This apostolic covering is the covering of Christ.
You can read more detail about this in "How Does Apostolic Covering Work?" - and cover this concept in depth in Chapter 7 of "The Apostolic Revelation" book.