I know it is a branch in pentecostalism, but that's about all I know.
From Wikipedia- http://en.wikipedia.org/wiki/Third_Wave_of_the_Holy_SpiritThe Third Wave of the Holy Spirit is a Christian theological theory first introduced by C. Peter Wagner to describe what he believed to be three historical periods of the activity of the Holy Spirit in the 20th century and beyond. In his 1988 book, The Third Wave of the Holy Spirit: Encountering the Power of Signs and Wonders Today, Wagner defines the three waves as follows:The first wave at the beginning of the twentieth century with the rise of the Pentecostal movement, beginning with the Azusa Street Revival; A second wave during the 1960s as the Charismatic movement spread throughout some Protestant denominations, as well as the Roman Catholic Church; and A third wave during the mid 1980s. End QuotesI would also add the following information to bring some perspective. In practice most Third Wavers are open to the baptism in the Holy Spirit and the experiences that often accompany it. However, unlike classic Pentecostal theology they do not believe that tongues are necessarily an initial physical evidence of having received that experience. Third Wavers would generally agree that tongues may often accompany that experience....but is not the specific nor only evidence. Third wave theology more closely believes that an empowerment of the Holy Spirit to perform signs, wonders, and evangelize in that same power, are the marks of having received that Holy Spirit baptism.I also might add that third wavers embrace a wide theological spectrum. I am personally friends with ministers that are third wave charismatic leaning and others who are third wave full five point Calvinists. Another thread brought up the issue that ones soteriology has little to do with their views on this issue of the Holy Spirit. I have found that to be particularly true in the case of Third Wave theology.
I wrote a brief paper on "The Third-Wave Movement" when in Bible college. Consider the following paper: http://www.iamadisciple.com/articles/papers/TheThirdWave.pdf