It is Greek Fru ...
The first half logor has as it's root word "logos", which means "the spoken word" (lotsa meanings, but that is the shade of it in this case)
The second half "rhea", means "continuous flowing" ... as in the example of diarrhea.
So logorrhea technically means an endless flow of words.
Using my Google and wikipedia-fu, I came up with this:
http://en.wikipedia.org/wiki/Logorrhoea
The word was used to describe the inane babblings of the mentally disturbed, and came to be applied to anyone who was regarded as talking constantly about nothing.