The Power Booster Rod was created when Dargon Chesterfield wanted to escape his universe - or more specifically, The Cheese of his universe. Opening a portal into the Walkyverse required a mass displacement equal to that of him and his troops back into his own universe to prevent its heat death. The difference was teleported as energy (Energy = Mass × (Speed of light)² -- that's A LOT of energy!) into a tree branch that happened to be lying nearby.
Rather than surrender the branch to The Cheese, Dargon took it with him, condemning his home reality in the process.
After entering the "prime" Walkyverse, it became obvious that the Power Booster Rod was not very powerful in the hands of humans. To meet their needs, the JFO killed Linda Walkerton, then resurrected her using a Martian Resurrection Chamber, splicing Martian DNA into her human genes. She was then brainwashed and tricked into using the Rod to kill all of the Martians. The Rod eventually passed into the Head Alien's hands, and later to SEMME.
Depending on the wielder's will, the Rod can fire energy blasts or cover a large area with yellow energy that can be ignited at the wielder's command, destroying anything and everything within it. The area affected depends upon on the inherent power of the wielder - a human can cover little more than a small room, whilst Sal turned the entirety of North America yellow.
The Cheese can sense the use of the PBR, hinting that the energy manipulates the universe in a way he is sensitive to. It was used by Joyce Brown to call upon the Cheese twice, much to his displeasure. When inhabited by the soul of David, the Cheese was unable to use the Power Booster Rod to much effect, but when inhabited by Walky, he was able to turn the Earth completely yellow and make the Martian forces vanish. This suggests that the usage of the Power Booster Rod is related to the Martian psychic ability and the properties of the wielder's soul.