The Unity Engines are powerful devices created by Sigma-1 in order to draw upon the power of worlds such as Mobius and Earth 20XX in order to grant him greater power. They accomplish their purpose by linking and then fusing worlds together, and channeling the power thus accessed into the Master Engine, which in turn feeds the power into Sigma.
After conceiving the idea of the Unity Engines, Sigma set Dr. Ivo "Eggman" Robotnik and Dr. Albert W. Wily to work building them in his base on the Lost Hex. As Sigma contemplated the power the engines would grant him, he wondered what his old foe X would think of him after the engines granted him the power of the two worlds he was seeking to conquer. After Sonic the Hedgehog and Mega Man were captured and turned into Roboticized Masters Sonic Man and M'egga Man, each was sent to the other's world with a Unity Engine to place in Mega City and Mobotropolis, respectively. Despite some initial resistance from Break Man, Knuckles the Echidna, Quake Woman, the Knothole Freedom Fighters, the Light Robot Masters, Gemerl, and reformed members of Wily's Robot Masters, the two corrupted heroes managed to set up their engines. The machines began fusing the two worlds together with devastating consequences for the inhabitants, while Sigma was empowered by their energies. Sigma thus anticipated gaining control of the Genesis Portals and all of reality, while the restored heroes and new allies such as X set out to stop him. (SU: #76; SB: #8; StH: #273; MM: #50)
After linking up with the heroes, Eggman and Wily revealed Sigma's master plan: to merge other worlds together using other Unity Engines and thus gain unimaginable power. However, Sigma's enhanced power came at the cost of destroying the worlds thus fused by the Unity Engines, though with a delayed effect to enable him to absorb as much energy as possible. (SU: #77)
The Unity Engines are designed with technology from the future of Earth 20XX, which by some means enables them to fuse worlds together. They are designed to harness the energy of worlds and feed them into the Master Engine, which in turn feed it into Sigma. According to Sigma, employing an engine on a single world would cause rapid destruction, such that the planet would be destroyed before any power could be harvested from it. As such, fusing two or more worlds is ideal for Sigma's plan.