The TI-84 is a graphing calculator by Texas Instruments (which is what the TI stands for). It comes in three editions: the TI-84 Plus, the TI-84 Silver Edition, and TI-84 CE. Each comes with all the standard functions that a graphing calculator can have, including the loading of custom dedicated programs. The TI-84 CE runs a different operating system than the others (it's backlit as well), so programs on the CE likely will not run on the Plus and vice-versa. The one I bought says "school property".
The difference between the regular, Plus, and Silver is the amount of RAM they have. The Plus comes with 24 kilobytes of RAM for loading programs (128 total). The Silver expands the RAM to 154 kilobytes of user-accessible RAM (something that I wish I knew before I bought my regular one. A friend just said "don't get the silver, it's worse" and I took his advice without researching it.)
You can load many programs onto it. Someone made DOOM on it, and someone else made Tetris, and there's a bunch of big-boy math programs too, which is the intended use of course. (I loaded Tetris on mine just for gits and shiggles, but never actually used it.) I bought this before going into my second university math class, thinking "I will need this". I have used it maybe once for graphing, everything else has just been regular scientific-calculator stuff, like the quadratic equation.