A sound wave is a pressure vibration caused by the movement of energy traveling through a medium e.g. air, as it propagates away from its source.
As sound passes through the air, the air particles move left and right due to the energy of the sound wave passing through it. It's the vibrating air molecules that cause the human eardrum to vibrate, which the brain then interprets as sound.
Air molecules do not travel from the noise source to the ear. Each individual molecule only moves a small distance as it vibrates, which causes the adjacent molecules to vibrate in a rippling effect all the way to the ear.
Sound waves are longitudinal and should not be confused with transverse waves. Most waves are transverse, including light and the ripples we see on water.
Transverse waves vibrate at 90 degrees to the direction of the wave. In contrast, longitudinal waves have vibrations along the same axis as the direction in which the wave is traveling. Think of the way a slinky behaves if two people are holding each end and one person quickly sends a number of vibrations down it.
Compression happens in the region in a longitudinal wave where the particles are closest together. Rarefaction is a region in a longitudinal wave where the particles are furthest apart.