Sound falls under that class of physical phenomena which is the transfer of energy through waves. Energy which is transferred this way is done in one of two kinds of waves: either mechanical or electromagnetic waves. Mechanical waves must travel through some kind of material (called the medium); electromagnetic waves can travel through vacuum. The most easily recognizable form of electromagnetic waves is light. In any case, waves are all initiated by something which is causing a vibration.
Mechanical waves can further be broken down into two categories. Mechanical waves can either be transverse waves or they can be longitudinal (also called compressional) waves. To get a handle on what transverse waves are like, imagine a rope being shaken up and down quickly or a wave traveling across the top of water. The wave goes up and down as it moves from the source of the vibration. The direction the wave travels is perpendicular to the direction of the vibration. Transverse waves always have the direction of vibration perpendicular to the direction of travel. Longitudinal waves are made of alternating regions of compression and rarefaction (separation). Imagine a spring being squeezed and released. The compressed part of the spring seems to move along the spring. This is the characteristic of longitudinal waves: the direction of the vibration is in the same direction as the direction of the wave.
Sound is a longitudinal mechanical wave. Sound must travel through a medium. Sound can travel through several kinds of media including air. The energy which is being transferred as sound begins as a vibration of matter (vocal chords, guitar strings, drum head, etc...) which compresses and rarefies the medium. This compression moves away from the source of the vibration. In the case of sound traveling through air, molecules of air are compressed together by the vibrating object as it moves into the air, and then pulled apart as the vibration moves the other way. This alternating compression compresses adjoining air molecules and that compression is passed on to adjacent molecules moving away from the source.