The 84 Plus has more ROM/Flash memory than the 83 Plus and a slightly better display. This is useful for storing flash applications. The 84 Plus also has a face-lifted appearance, and is slightly bulkier in design. It also costs more than the 83 Plus.
Both calculators are capable of graphing functions and equations, solving matrices, and other mathematical functions, making them useful for Algebra, particularly higher level Algebra. Both are also capable of being programmed to do various tasks, and, most importantly to high school students, they can be used to play BASIC and Flash games (ie Space Invaders, Falldown, Uncle Worm, etc.)
Person 2: Yeah, but you better give it back. <hands calc to friend>
Person 1: You've got an 84 a TI-84 Plus? Sweet. Lemme see what games you have.
Person 2: Hey, I thought you needed it for math class...
Person 1: Well, duh. What do you think I do in math all period?