They add bonuses to habitibility/max pop, plus food and mineral production. I don't know the details about the food & mineral bonuses. (Nor the habitibility and pop bonuses, but I think the details on the pop bonuses may be known.) The pop increase can be great from large moons, making huge Industrial planets with two Industry DEAs in a region possible. (Normally, two Industrial DEAs in a region together require so much pop that there isn't enough to make upgrades worthwhile, because they increase the pop required.) Never played a game long enough to see that yet,
but I've heard it's great.
Also, they increase the maximum number of orbitals you can build around a planet. 3 more orbitals per moon, IIRC.