If you attack a world and can't get it down to 1 pop because you ran out of energy or you disabled your ship against it that is when you use one. Because if you don't by the time you have more energy the pop of the world would of have gone up since you left making it harder and making it take longer for you to take the pop down. Instead of it growing when you leave it will do what Razorback said and just stay still at that number till the 24 hours are up. However if the other player is on and see's it he/she may use a Cloning Pod in order to get his pop back up to full health. This is why most players use them at the start of the match because if you start attacking a world and you all most get it down to where you can invade and the other player comes on and starts to guard it then they usually heal the world once and then put the artifact on that makes the world immune to artifacts so the player attacking can't use a warp gate to take them off. If they do this then while it sucks having to fight the world with the player on it you can take a whole day because the pop will not regenerate and they will not be able to heal it because of the immunity. Now in this case be prepared though because once you get the worlds pop to the point where you could invade now you have to take out the player guarding the world as well. This is when a legion really comes in handy. Because if you try to do it solo the player could justs keep on putting on traps making it imposable to take the world where as if you where in a legion your legion mates could help attack the player and/or eat traps so you can kill the player. If you are the one trying to take the world it is better if you do not hit traps because a KV and a H trap will make it either imposable or not very probable for you to take the world. Once you take the world be ready to defend it again because the other player will try to take it back if it was worth much. Most of the time it is wise to be sure to have a planet flux with you before you take a world that way you can flux it away from the player as soon as you take it making it so they can no longer see the world and take it back. Be ready though because if the other player alerted the world to their legion then they can still see the world even if it was fluxed until the share timer goes off.
Hope this helps I know it is a lot more than what you are looking for but by your question I'm guessing you have just started and that you don't know much about how the game works. That is why I went all out on my response. lol Good luck and have fun.

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Please check out my path guide:
http://galaxylegion.com/forum/viewtopic.php?f=3&t=30938Ship size: Colossal Galaxy Destroyer,
Because just destroying your star wasn't enough.