To understand boosters though, we'll need to look into the game's setting a bit first. The thing to remember is that as a player, you're a capsuleer. You're not standing on the bridge of your ship barking orders at subordinates. Rather, you're floating inside a metallic capsule deep within your ship. Your mind is interfaced with the ship you pilot via neural implants, thus your vessel is an extension of your body and its senses; you regulate the ship's activities merely by thinking about them. Not all people in EVE's setting of New Eden have the raw potential to become a capsuleer, making your character one of the elite. However, when faced with others of your caliber in combat, every possible edge you can gain over rival capsuleers helps. That's where boosters come in... they're your edge. Boosters augment aspects of your mental processes and thus provide certain bonuses when piloting your ship.
Over at EVE Tribune, writer (and recreational pharmaceuticals enthusiast) Kirith Kodachi has put together a good primer on boosters called "EVE's Little Pick-Me-Ups." He introduces what boosters are and how they function in the game. The article also includes tables of bonuses imparted, the possible side effects, and the relative strengths of each booster type. "EVE's Little Pick-Me-Ups" is a great introduction to this aspect of the game, and there's more to come. Kodachi writes that next week's article will "look into the mysterious processes involved in booster manufacture." If you're curious about this side of EVE Online, EVE Tribune's series of articles on boosters will definitely be one to watch.