The "science" behind binaural beats is unfounded. (
http://skeptoid.com/episodes/4147) There's nothing binaural beats can do that music in general can't.
In general, anytime people talk about something that was discovered in the 1800s and "earned greater public awareness in the late 20th century based on claims that X could help induce...desirable mental states" it's almost certainly entirely void of any factual basis. I'd be willing to wager that someone came up with this to try to make money. Homeopathy (ie: a kind of placebo) is another good example of this kind of thing. 19th century science was pretty seriously flawed