Is it what was prescribed in the Koran of muslims and what is called 'The New Testement' of christians that has given these peoples the ability to gain conversions and great swaths of land? The Roman Empire, when combined with Christianity flourished because of the roman bureaucratic organization combined with intermarraige among the conquered and probably forced conversions. Jihad, one of pillars of Islam, provided incentive to conquer lands and people. Forced conversions also surely played a part. Was it the religious tenents as they were written and followed by their adherents that caused populations of Christians and Muslims to be able to possess a lot of land, fight to obtain and protect it, therefore evolving to produce the large populations of Christians and Musims we have today?
It is fundamentally the result of empire-building and the conversion of "conquered" or "subject" peoples. This animated map shows the spread of religion around the world from c3000BCE to 2000CE.
Wikipedia offers this page on the Growth of Religion which attempts to explain the current, rather than historic, trends.