To divvy something is to split it up between two or more people. You might divvy up a pizza among four friends, giving everyone two slices.
If you and a friend have a lemonade stand, you'll divvy up the proceeds at the end of the day, sharing the money. You can also divvy other things: "Let's divvy this painting job — you do the trim, and I'll paint the walls." As a noun, a divvy is a share or a part of something — the word, from American English, is a shortened version of dividend, a divided payment, from the Latin dividendum, "thing to be divided."