Let's say New Orleans insists on getting rid of Okafor and his bad contract (as has been suggested). Let's say Orlando has a deal with New Orleans for Paul, but they don't want Okafor because they have Howard and Lewis. Here comes Toronto with their TPE. They offer to take Okafor off of their hands, and for their troubles, Orlando also gives Toronto a 1st round pick for some trash (Alabi or Jones).
New Orleans receives Gortat, Nelson, Orton, 11.5 million TPE
Orlando receives Paul, Alabi/Jones
Toronto receives Okafor, 1st round pick from Orlando
I'm NOT suggesting that New Orleans would take this, just showing you how the TPE could help in facilitating a deal. Does that make it more clear for you?