Why the Sixers do it:
Thad is playing great team defense and doing Thad-like things on offense (finishing around the basket and missing jumpers). But the Sixers have an obvious need for size and skill at the 4/5 positions, and Cousins provides more of what the Sixers need than Thad. He is also 22 and has more upside. If Bynum doesn't come back, they can avoid using the Lavoy/Hawes/Kwame triumvirate at the center position. If he does, the Sixers have two skilled big men under the age of 26. Taking back Garcia's contract is worth it.
Why the Jazz do it:
They are going to lose Jefferson this summer anyway. Receiving Thad (to add athleticism and versatility to their 2 young bigs) is worth taking back Salmons' contract. And Salmons can still be a serviceable player for a playoff team.
Why the Kings do it:
The trade hinges on what the Maloofs think of Cousins. He is playing considerably worse than he did last year, even though he stayed in great shape. He already has one suspension and the next one feels imminent. The Kings are an absolute mess and they might not be in Sacramento for much longer so it's very difficult to project what the Maloofs want to do with him. But if they assume that he will walk after his rookie contract (which seems likely) they might jump at the opportunity to lock up Jefferson (just 27 years old and a good teammate) to a long-term deal, while getting rid of two bad contracts.