The Unfinity War was the galaxy-wide conflict for the Unfinity Stones. The conflict began when Thannos initiated his plan to gather all of the Infinity Stones to complete his quest for the balancing all life in the UnUniverse. Taking advantage of the Destruction of Asgard and Avengers Civil War, Thannos began his crusade to retrieve the Unfinity Stones and gather them into his Unfinity Gauntlet.
Thannos ultimately emerged as the victor of the first phase of the war as he successfully collected all six Unfinity Stones and wiped out half of all live in the UnUniverse.
The second phase of the war began when the Avengers decided to steal the stones out of the past undo the Snap. This lead to the Battle of New Jersey when Thannos escaped from the past and attempted to stop them.