C. Peter Wagner invented the term "New Apostolic Reformation" and then pronounced himself God's appointed leader of it:
“I needed a name … For a couple of years I experimented with ‘Post denominationalism’. The name I have settled on for the movement is the New Apostolic Reformation.”
(Source: C. Peter Wagner, The New Apostolic Churches, Ventura CA; Regal, 1998, p. 18.)
It's a loosely knit association of churches and ministries on the outer fringes of anything resembling Biblical Christianity. Supernatural Signs & Wonders; Dominionism; The Latter Rain Movement; Joel's Army; The 7 Mountain Mandate; Third Wave Revivalism; IHOP; Bill Johnson's Bethel Church, The Hillsong Media Empire, Rick Joyner's MorningStar Ministries... these are all a part of this shape-shifting movement in one way or another. It is gobbling up churches and deceiving millions around the world.
Some key beliefs of the NAR: We've entered a "2nd Apostolic Age" (starting in 2001); the church should somehow take over the world (dominionism); a great end time harvest/outpouring will occur once we battle enough demons, perform enough miracles and unify under these new Apostles; God is giving new revelation to his Prophets/Apostles but they will make many mistakes in the process and that's okay, but following the Bible too closely makes you "religious" and narrow-minded...
Here are a number of different articles from different theological and denominational backgrounds that all agree that the "New Apostolic Reformation" isn't new, isn't apostolic and isn't a reformation: