The Yankees traded Martin Prado and David Phelps to mostly get Nathan Eovaldi from the Marlins; that was their prize. However, in order to make up for losing Prado, they needed another bat who could play backup at multiple positions, which is where Garrett Jones came in. The Yankees didn't just see him as another 1B/RF bench guy, they saw him as injury insurance against all the players who will likely get hurt at some point this season.
As everybody insurance, Jones will be there in case any of Mark Teixeira, Carlos Beltran or Alex Rodriguez suffer any kind of serious injury. The Yankees finally saw it worthwhile to have a true backup first baseman and not just someone who they can chuck in there and hope survives. Jones isn't exactly a wizard with the glove, but he has nearly 4,000 innings at first base and won't be a liability out there. If Tex goes down for a month, that's what the team will need, not A-Rod or someone else trying to figure out how to scoop an errant throw. Remember the Kelly Johnson Experience?
A huge concern going into the offseason was how the Yankees would defend against the possibility that a 37-year-old Carlos Beltran might get hurt again in 2015. They wasted no time re-signing Chris Young, but if Beltran went down for an extended period of time, they were going to need someone else out there. One of Prado's many talents was his ability to play in right, making him extremely valuable as an outfield backup, both in case of injury and in order to ensure that Young doesn't get too much playing time. With Prado gone, the Yankees needed someone who could take his place as placeholder in a damaged outfield. Garrett Jones has over 2,000 innings in right field, and though he isn't rated especially well out there, he'll likely be better than an old Beltran and should be able to hit enough to make him worth it.
Now that Alex Rodriguez has been dethroned as the starting third baseman, he'll likely be used as the everyday designated hitter to start the season. The hope would be that he could finally remain healthy if he has a less intensive year in the field, but the man hasn't stayed off the DL in years and having a competent backup will be a necessity. Jones hits for more power than Prado and is less of an extreme strikeout/home run hitter than someone like Mark Reynolds, making him a serviceable DH in the event that A-Rod once again gets put on the shelf for a long period of time. Now that Prado is gone, A-Rod will have to be the backup third baseman, and if he has to fill in for Chase Headley, Jones can easily slip in at DH for the time begin.
Jones struggles against lefties, but with Brian McCann also able to play first, Young in the outfield, and any number of players able to fill in at DH against the occasional tough southpaw, the Yankees' newest addition should fit in quite nicely when he's needed. If the last two seasons are any indication, Garrett Jones will likely be needed a lot.