I've seen this chess saying a few times and have recently been discussing it with a couple of my chess friends. Patrick Wolf explains it in The Complete Idiot's Guide to Chess. Rustam Kasimdzhanov points it out in his DVD Attacking the King for Experts. Karsten Mueller includes the advice in his book (with Dieter Meyer) and DVD, The Magic of Chess Tactics. In his book The Wisest Things Ever Said About Chess, Andy Soltis attributes a variation of the saying generally to the Soviet School of chess. Mark Dvoretsky and Artur Yusupov make a whole chapter out of the significance in their Secrets of Positional Play, even adding more specific guidelines to the advice.
Whoever said it first, there's no doubt a useful idea in it. Whereas opposite colored bishops tend to be drawish in the endgame, being strong on a color on which your opponent is weak can be a basis for attack, and this is what can happen in a middlegame with opposite colored bishops.
So with all this in mind, it caught my attention when I saw this conclusion in a book I just received today: "Some forms of compensation are: An attack with opposite colored bishops ...". The book is Danish Dynamite by Mueller and Voigt and the situation they are talking about are middlegames that sometimes arise from the Danish Gambit. Here's an example arising from the Queen's Gambit Declined from Chess Strategy for the Tournament Player by Lev Alburt and Sam Palatnik for you to consider: