Laudatory has to do with praise. If you do great things, then you've done praise-worthy acts and people will use laudatory words when talking about you.
We all probably do something laudable at some point. If you play baseball well or just keep your room clean, then you probably receive laudatory words of encouragement. If I say, "Your dog is the cutest, nicest pooch in North America," I am saying laudatory things about your dog. When you see laudatory, think praise.