Nothing happens that you can see. However, if the page that posted the image receives a TON of comments (even if they all say “jump” or whatever), then that page gets a boost in Facebook’s visibility algorithms. So, the people who liked the page are more likely to see posts from that page in their newsfeed.
In other words, it’s a manipulative marketing ploy. The people who type “jump” momentarily feel foolish, and the page gets increased visibility.
By the way, some of these actually say, “Type L and see what happens!”. What a lot of people don’t realize is that typing L is a shortcut to liking something – and liking a page means sharing your personal information with it. So, think before you type. ;)