This has come up in a number of my games recently and it took me a few tries to get it right, but I think I finally have this figured out.
So Contraband gives you extra economy and a buy for less than the price of Gold at a cost: basically you can't buy any good cards. And Advisor/Envoy are usually really powerful draw cards for their price, except that you usually can't draw any good cards. Well it turns out that this results in a really interesting synergy!
What better way to flood your deck with bad cards than to get lots of Contrabands, and if you reveal three bad cards with Advisor, your opponent is forced to make you discard a bad card! This turns Advisor into a powerhouse! The funny thing is that your opponents will usually not even catch on to what your doing and continue to ban good cards to your Contrabands, then when they've lost to you they don't even get why. They probably haven't heard about this combo, so they don't realize the immense value you're getting out of your Advisors.
The same thing works with Envoys, though it's a little harder to pull off because you typically want to have Villages in your deck to pull it off, and as we all know, Village is the strongest card in Dominion, so it's easy for them to ban it. Even the least competent opponents know that.