Ok after some brief research, I think I have basic idea of how it works. As far as I can tell, the Game Genie is the only product out right now (No Pro action replay, gameshark etc.)
What the Game Genie does is edit save game data. This is a bit different from what you think of when you think Game Genie for older systems (NES etc). The way it worked in the old days is that the Game Genie would actively edit the data that was being used in RAM. When you start a game, the system reads everything off disk or harddrive and runs it all in RAM, only using the disk after to load whatever it hasn't already. Doing so allowed you to change how the game ran which allowed you to do things like have invincibility or infinite ammo.
That's not the case in recent years. Securing RAM and access to the systems that write to RAM has become a huge priority to fight off piracy. Without hacking the system, you can't do things like we did in the old days with cheat devices.
This Game Genie takes another route, it edits the data saved in our save files. From what I can tell, this product comes with a USB drive to transfer save files to and from the PS3. You then load them up on your PC, use their software to edit the data, then transfer back to the PS3.
Doing it this way, you can only edit whatever is stored in the save file. Think how much money you have, the stats of your characters, or bonuses you've unlocked in the game. Still cool, but not as pervasive as we might be used to.
There's a couple caveats with this though. Each game encrypts their save files differently. That means that before you can edit the game save, someone has to figure out how to decrypt that particular game. Luckily, this seems to be going a lot easier now than in the past. According to their site, there's 433 games you can edit at this point. Apparently their update process is pretty good too so they get pushed out once they're approved by the manufacturer (which seems to be Hyperkin?).
I don't have the product on hand so I can't say how user friendly this all is, but I'd be inclined to believe it's not that hard and they walk you through it. You can even download save games from other people to use.
From a video I saw, this could lead to unlocking trophies easily. I don't know if this would lead Sony to banning some PSN accounts or not. I imagine the Game Genie doesn't have codes for online/multiplayer games as that'd probably get people banned and enable cheating online. So in reality it's probably safe to use, especially for single player games.
I hope this helps!