Recent research at the University of Lisbon finally uncovered the reason for the 350 year-old mystery, finding that the resonance of sound is the mechanism for entrainment of swinging pendulums and ticking clocks, and it seems likely that the energy transferred by sound is also responsible for other observations of entrainment, including brainwave entrainment.

This is a question I have noticed to concern many people, who are researching the issue. I have come across this question in forums, Yahoo Answers, in blogs, and all other sorts of  places. I can definitely empathize with someone who is looking to find a solution to a problem like anxiety, migraine, pain, etc., and needs reassurance and scientific proof that brainwave entrainment actually works!
Neural oscillations are rhythmic or repetitive electrochemical activity in the brain and central nervous system. Such oscillations can be characterized by their frequency, amplitude and phase. Neural tissue can generate oscillatory activity driven by mechanisms within individual neurons, as well as by interactions between them. They may also adjust frequency to synchronize with the periodic vibration of external acoustic or visual stimuli.[3]