Cachinnate sounds like what it is: it's what you do when you laugh loudly, guffaw, or cackle, and probably embarrass or annoy everyone around you.
Cachinnate isn't an everyday word, and you're most likely to come across it in literature — or on vocabulary tests. Cachinnate, comes from the Latin verb cachinnare, which also means "guffaw." Despite the word's ancient pedigree, it doesn't appear in English until 1824.