Globe has to perform. The assignment is occurring between Baxter and Clay (a third party). Baxter says to Clay, “Hey, I have contracted with Globe to buy a couch, but I don't want it anymore. Do you want to buy this contract from me?” Clay says, “Yeah, sure, I really want a new couch, I'll pay you $X for your contract with Globe.”
At this point, Baxter = assignor, Clay = assignee, and Globe = obligor (he is OBLIGATED to perform/to sell his couch to Clay). Baxter is off the hook! He sold the contract to Clay, Clay paid him consideration. However, if Globe leaves the country and never gives the couch to Clay, Baxter is liable. That is the only way Baxter would still be liable. Therefore, the only way he would NOT be liable anymore is if Clay released Globe.
You asked “If Baxter is the one liable, why is Globe being released?” The answer is because the contract is now between Clay and Globe. Baxter is only liable if Globe does not perform. Thus, if Clay lets Globe off the hook (“releases” him), then Baxter is off the hook too. A release is when one party relinquishes his right.
That may have just confused you more, but that's the best I've got!