Cutting A Melon
  
There are two difficult things about cutting a melon. First, you need to be able to determine whether the melon in question has reached optimal ripeness. And second, you need to know what to do about the rind.
(Please excuse the previous paragraph. It was intern day here at Shmoop and the current crop of undergraduates has been...disappointing. We now return you to our regularly scheduled writer.)
"Cutting the melon" is financial-world slang for when a company provides a dividend above and beyond their normal dividend. The melon represents the company's profits. The cutting of said melon represents the divvying up of those profits.