Oh no problem. TO succeed something or someone is to come after or follow it. So in this case it just means that Aurora and Corona come after Celestia and Luna. They succeed them as princesses. Hope that clears things up for you!
I would certainly like to know more about them my self! They develop a little more each time a I draw them. And the comic is just supposed to imply that Celestia's love of sweets passed on to Corona...somehow...I thought it was funny.