Sound does not travel through a vacuum because molecules of matter are required for sound to exist, and vacuums do not have any matter. The vibrations and movements of small particles of matter are what create sound and allow it to be heard. In a vacuum without any matter, such as space, it is impossible for sound to travel.
According to How Stuff Works, sound is a longitudinal wave. It is created when a movement causes vibrations in its surrounding molecules, usually a gas or liquid. The vibrations spread outwards from the molecules, gradually getting weaker but pulsing outward. Without the matter of the surrounding areas, sound would pass. When these traveling vibrations reach someone's eardrum, they are transferred on to small hairs. These hairs are able to interpret the vibrations and convert them into messages which are relayed through nerves to the brain.
However, in a vacuum, one of the first and most vital steps of this process is missing. Vacuums do not have the prerequisite molecules of matter for vibrations to occur. No waves are transmitted through the movement of molecules. Without these vibrations passing through any gas or liquid, they cannot ever interact with the inner ear. This property makes it so that it is impossible for sound to pass through a vacuum.