AI War:Command Posts
What Do Command Posts Do?
Command Posts was a pre 4.0 name that has been replaced by the term Guard Posts
Guard Posts and are now specialized into many different types and current information on them can be found here: Guard Posts.
The pre 4.0 answer
A: Firstly, they block resource gather points. More importantly, when an AI reinforces a planet, it gets units at each command post. By killing the command posts, you cut down on the volume of reinforcements the AI is able to get at a planet. In order to get reinforcements, however, the AI has to have a command station or warp gate at that planet, so if those have already been destroyed then you are at no risk of more reinforcements arriving, anyway (excepting some cases like Special Forces Guard Posts, which spawn their own units).
Another consideration with command posts: normally, ships that are guarding each command post won't stray too far from it unless chasing an enemy ship that came within their range. However, when the command station on the planet is destroyed, there is about a 50% chance that all the guards will decide to abandon their posts. With low-level planets this matters little, but if you are attacking a Mark IV planet and have not cleared off all the command posts before taking the command station, you have a 50% chance of getting a nasty surprise. Even worse, if the released guards kill all your forces on their planet, they will then swarm over to your planets, destroying whatever they can. With higher-level planets, this can lose you the game if you aren't careful about it.
A higher difficulty AI will also react differently with those now-free units. The higher the difficulty, the more accurately the AI gauges its forces against yours in deciding if it can win. It will send its units against you immediately if it thinks it can, otherwise the units will retreat to become part of a Cross Planet Attack later.