Amazon Prime has many perks, but our two favorites are access to instant streaming to movies and TV series (decent ones, too! We've recently started watching Parenthood - which is a terrible idea if you're pregnant. It's an awesome perk for all of us who've axed cable service to save some money) and free 2-day shipping on eligible items (which is basically everything, unless it's sold by some obscure seller).
To sign up for Amazon Prime for students, you'll need to use an email address ending in .edu, and enter things like your school, graduation year, major, etc.
We've had Amazon Prime for students since just before Christmas my husband's first year of med school, and we honestly have used it more than I anticipated, for everything from his books to buying Christmas presents. I'm pretty certain that we'll have it long after he's done being a student (which apparently does happen at some point, right?).
Any questions, just ask away!