I for my first time got one (thanks to the bug where you can board anything, and the fact it had only 10 components unbuilt when I found it, thanks to the weak AI that had his homeworld only 2 systems away...)
And at first my reaction was: "AWESOME!"
Only to realize that it cannot conquer planets (it has no troops), it cannot explode planets (it has no bombard action), it cannot steal ships (it does not has boarding pods), and its superweapon is ****... I sent it to fight a lonely station, and it damaged the station much faster with its normal weapons (and it still lost and had to jump away to recover shields).
The only thing it did nice, is kill escorts very quickly... but other than that, what is it for? (beside breaking your firepower count and making your AI stop making ships even when you have 300k of positive money influx)
The world destroyer destroy worlds aka planets. They vaporize them. Also, you have to wait it charge.
Just tell him to attack a planet and it should start the countdown.