Have you turned on the squares?
This topic should have [spoilert] in the title since figuring out how to play it is part of the game itself.
When you fire your laser, the green thingy also fires some sort of laser against the red square below the purple square (the goal) in the upper right corner. You have to make a path with the arrows that's long enough for the green laser to hit the red square so it can disappear so when your laser comes there it won't be stopped, but reach the goal. And don't forget to activate the white squares so they become red, otherwise the laser will run out of energy.