While The Grid and Unidentified Overlord Cannon were defensive means, this power station was meant to supply an offensive weapon for the Espheni. It was meant to attack the race that drove them from their own galaxy and who are currently approaching Earth and the surrounding star systems.(The Eye)
The station is later revealed to be both a mining platform and refinery, drawing Helium 3 from the lunar surface and converting it into wireless electricity that would be beamed down to Earth, powering all Espheni technology. It is placed on the Moon since its location in orbit allows it to cover the entire planet. While it is unknown what the Espheni used to power their technology before the station's construction, by the time of its discovery, they were totally dependent on it for power as destroying it irrevocably deactivated their technology.
The green flashes from the power station weren't noticed until a few years after the Invasion of Earth began, indicating that they weren't that frequent at first, even after the station was constructed. Indeed, its commented in Shoot the Moon that the frequency of the flashes increased from every 60 seconds to every 10 seconds. It is unclear why the flashes would come more often at that point but they are also visible in the daylight if one is looking at the Moon.
While it is unseen, the Espheni have a base near the power station on the Moon for their Beamers. Presumably it was built to supply and protect the station from any sort of attack. Any Beamer that is flown manually above the Earth's atmosphere will lock onto the homing beacon from this base and fly there as shown with the 2nd Mass' Beamer in Space Oddity and Shoot the Moon.
The station, generally referred to as the Espheni power core or just the power core is first mentioned by the Volm who are searching the planet for it due to the tactical advantage of destroying it. They have no luck in finding it until the end of A Thing With Feathers when light from the Moon activates a shot-down Beamer and Tom and Hal Mason notice green flashes coming from the Moon. Examining it, Cochise realizes that the flashes are coming from the power station and is angry that he never thought to look there as the Volm had searched the Earth with no luck and the power station was over their heads the whole time on the Moon.(Til Death Do Us Part)
Following the discovery, the 2nd Mass quickly realize that there's only one reason the Espheni would place their power station on the Moon: to cover the entire Earth and power all their technology there meaning the power station is the key to their war machine that gives them the advantage over humanity. Realizing this, Tom decides that rather than strike Ghettos and Skitter factories one at a time, they need to destroy the power station and knock out all of the Espheni technology at once. To this end, he decides to unbury the Beamer that alerted them to the power station's location and use it to reach the Moon. While the rest of the 2nd Mass thinks its crazy, they agree to try, eventually unearthing the Beamer with Mira's scout whistle, the first step to reaching the station.(Til Death Do Us Part)
The 2nd Mass learns from a recorded message of the fact that humanity is on the verge of extinction due to an unstoppable new weapon the Espheni possess. While the message suggests they go into hiding, Tom is still determined to destroy the power station, seeing it as their only real chance of survival and the only hope to win the war. Tom is able to convince the 2nd Mass to continue with the plan to destroy the station despite it being rash and desperate and a way to pilot the Beamer to the Moon is figured out. Tom and his son Ben Mason are chosen to fly the mission while a bomb is made to be deployed from the Beamer once it gets to the Moon. However, just before the mission can start, a Beamer squadron attacks Chinatown only to be destroyed by Lexi.(Drawing Straws)
Following the appearance of Lexi, she convinces her father to let her go on the mission instead of Ben, believing that the mission to attack the power station has the best chance of succeeding with her help due to her powers. Its reluctantly agreed to and Lexi joins Tom as they set out to destroy the power station. However, due to life support issues from damage to the Beamer, the bomb is destroyed and they can't use it. The Overlord Scorch captures the 2nd Mass' Beamer before it can reach the Moon with a much larger ship to stop them personally. Tom kills him with a Volm poison, but not before he destroys his ship's autopilot system with his dying breath. With no bomb, Tom decides to use Scorch's ship to destroy the power station, but Lexi discovers that the autopilot is destroyed. Discovering she can still pilot the ship manually with her powers, Lexi chooses to sacrifice herself to destroy the power station and says her goodbyes to Tom who she sets on course back to Earth in their original Beamer. As Lexi flies to the power station, a Beamer squadron from its defending base attacks Tom only to be destroyed by unexpected Volm reinforcements led by Waschak-cha'ab. With her path clear, Lexi performs a suicide run on the power station with Scorch's Beamer. The Beamer crashes into the middle of the power station, destroying it. The power station goes up in a massive explosion that turns part of the Moon green and is still visible from the Earth the next morning. The explosion also sends a shockwave into space that blows Tom's Beamer into deep space where he is rescued by the Dornia. As hoped, destroying the power station deactivates all Espheni technology on Earth including their farms, Ghettos, Mechs and Beamers.(Space Oddity) (Shoot the Moon)
Following the destruction of the power station and the loss of their technology, the Espheni are put on the defensive and humanity is finally able to begin successfully striking back. The Espheni retreat to bases in cities like Washington, D.C. and are forced to rely on their organic servants rather than their mechanical ones. Unless they are within a five-mile proximity, the Espheni are left with no control over their Skitters and Black Hornets as well and start relying on trickery, such as using clones of Katie Marshall and Alexis Glass-Mason to do their dirty work. Eventually their lack of technology allows humanity to defeat them in Washington, D.C. and win the war.