Laudatory means full of praise. It describes the speech, the review, the article, the letter — not the person. A laudatory review says the film is wonderful; a laudatory speech at a farewell party says the leaving colleague was excellent. The word is formal and rather bookish. You will meet it in newspapers, book reviews, and official writing, and almost never in normal conversation — friends say "he was really positive about it", not "his remarks were laudatory". It also carries a slight flavour of praise delivered publicly and at length, so writers sometimes use it with a raised eyebrow: describing a report as "laudatory" can quietly hint that the praise was a bit too generous, or expected, or paid for. Context tells you which. Note that it says nothing about whether the praise is deserved — only that praise is what is being given.