Rarefaction is the reduction of a medium's density, or the opposite of compression.
A natural example of this is as a phase in a sound wave or phonon. Half of a sound wave is made up of the compression of the medium, and the other half is the decompression or rarefaction of the medium.
Another natural example of rarefaction is in the layers of our atmosphere. Because what constitutes our atmosphere has mass, it is definite that most of the atmospheric matter will be nearer to the Earth. Therefore, air at higher layers of the atmosphere is considered to have less pressure, or is rarefied in relation to air at lower layers.
Rarefaction can be easily observed by compressing a spring and releasing it.