Binoculars come in 2 basic styles: porro prism and roof prism. In the photo below, porro prism binoculars are on the left, roof prism binoculars are on the right.
Below is a diagram of porro prism binoculars. (photo credit)
Porro prism binoculars are named after Italian optician Ignazio Porro who patented the system in 1854. Prisms extend the path of the light. This allows your binoculars to be about 9 inches long instead of much longer.
Roof prism binoculars have straight barrels, but that doesn't mean that the light travels in a straight path. Like porro prisms, roof prism binoculars have prisms inside that bounce the light off of the surfaces of the prism, extending the path of the light. Unlike porro prisms, roof prisms are stacked on top of each other. A common configuration, called the Abbe-Koenig prism, is diagramed below. (photo credit)
As far as the consumer is concerned, the main differences between the two are these:
Roof prism binoculars are generally lighter and more compact than porro prisms. They are also generally more expensive. Besides the size and price, there isn't a real difference in quality between the two.