The Twins claimed J.R. Graham from the Braves in the Rule 5 draft prior to the 2015 season. He remained on the Twins 25-man roster for the entire year (as Rule 5 claims are required to do), pitching 63.2 innings with a 4.95 ERA and 53 strikeouts. Graham has spent most of this season in AAA, only appearing in one game for the Twins where he gave up two earned runs in 1.2 innings pitched.
Graham was probably most recognized for wearing old-school stirrups. He did (and does) that so that his mother, who is legally blind, can pick him out from the other players on the field.
This move isn't really a big deal, and don't expect the Twins to get anything of real value in return. So what was the point? Paul Molitor indicated the move was made to free up space on the 40-man roster, so another move may be coming in the next few days.