Kelley, 31 by the start of next season, was heading into arbitration and the Yanks apparently didn't feel that the projected dollar value that he would be awarded (somewhere around $2.5-3 million) was worth it. Kelley struck people out but also gave up a ton of runs. He was either great or brutal and that general instability probably warranted the Yankees to try to move him.
Barbato is a hard throwing 22 year old that has 2 pitches, a fastball with movement that goes anywhere from 94-97mph and a sharp breaking curve. Both are considered plus pitches. He hasn't developed a 3rd pitch so the projection for him is a late inning reliever at this point. Some concerns about coach-ability but definitely has the stuff.
Yanks and Cashman trying to get younger either for a on the fly rebuild, or possibly accumulating assets for a big trade of some sort.