A 3 word story is when you take turns adding to a story with just 3 words of your own. Then it gets passed on to the next person.
For example:
Hello, my name doesn't matter. However,
So, the unbolded would be the first 3 words by someone else and the bolded would be the added words from the next person and it continues on until the story is finished with some type of "The End" or whatever.