To reunify is to bring a divided group back together in agreement or peace. Peace talks between feuding former allies are meant to reunify them.
The verb reunify is generally used in a political context, to describe what happens when two countries at war sign a truce, or when a divided territory is brought back together. Various events of the 1980s helped East and West Germany reunify, for example. The roots of this word are the "again" prefix re- and the Late Latin unificare, "make one."