Sociologists studying the movement - preeminently David Martin - suggest that the popularity of these churches is related to the way in which Christianity is linked to access to power. People are drawn to the neo-Pentecostal movement because they believe that their participation will result in some tangible results: financial success, health, successful marriage and so on. It is perhaps thus unsurprising that, generally speaking, individuals in less developed countries, particularly those making the transition from rural areas to large urban centers, are most likely to attend neo-Pentecostal churches.It's a telling analysis. People who feel powerless are drawn to power, especially egalitarian power. The pentecostal message of universal access to divine power is understandably attractive.
I'm ambivalent about the implications. On the one hand it seems like a terribly shallow motive. Going to church just for what it does for the self does little to reflect the sacrifice required of the believer. I'm often reminded of Acts 9:15-16, "But the Lord said to him, ‘Go, for he is an instrument whom I have chosen to bring my name before Gentiles and kings and before the people of Israel; I myself will show him how much he must suffer for the sake of my name.’"
On the other hand, Jesus' message was good news to the marginalised and the powerless. He preached to them, he showed kindness to them, and in the months immediately after his death his followers shared their possessions with each other. There is power in the gospel and it's hope for the powerless.
It's easy to see how it can become twisted, without violating the logic. The preaching of power to the powerless is one thing, but preaching it to the powerful is trouble waiting to happen. The hope for Pentecostalism is humility, the recognition of what they have and the responsibility to use that in the service of others. Without humility the movement will be utterly lost.