To send beings to the lost dimension
The Synchronizer was a raygun used by the other dimensional robots called Invertroids. With one shot, another being could be transported into the Lost Dimension.
When John Guardian was pulled into the mirror world by the Invertroids, he put up a fight and after knocking out several Invertroids, picked up a Synchronizer to use it against them. Guardian soon lived up to his name by staying behind in the mirror dimension to make sure the Invertroids would not return to bother Earth again.
The Synchronizers were first used in the episode The Looking-Glass Warrior.