Chances are your choice of hinge isn't something you'll have any say in, though it's valuable to understand the differences. The most important bit of knowledge to acquire is this: be sure to select cabinetry that offers a lifetime warranty on hinges.
There are three distinct types of hinges:
Concealed hinges (European cup hinges): These Euro-style hinges are hidden when the door is closed, providing a clean look for frameless cabinetry. Concealed hinges are typically attached through a hole bored into the back of the door. Easily adjustable, they often feature a "clip" that makes for easy removal and adjustments. Less easy, however, is its ability to open: concealed hinges only offer up to a 110-degree range of motion.
Barrel hinges: Leading the way in the realm of self-closing, spring-loaded options, barrel hinges provide ample access to the cabinet interior. Installed on the front frame, these hinges are fully exposed.
Knife hinges: Embedded in and screwed to the cabinet frame, this scissor-shaped hinge provides a 180-degress range of motion and is either fully or partially visible when the door is closed.