Manning, formerly Brad, now Chelsea, was sentenced for passing on information about US troops in the Iraq war to Wikileaks. The passing on was wrong, but exposed some brutality in the Iraq war that the American public should know, for example the helicopter attack on the unarmed group in the streets below it. Manning struggles with her transsexuality and has served over a year in prison. Obama could give her a pardon until Jan 20, 2017, upon which she would be released before Jan 20 (as conditions for the bet).
Obama could also commute her sentence to time served: the criterion for the bet should be if she's released before Jan 20, 2017, 12pm when Obama must leave office.