what is the difference between crests and rarefactions ,troughs and compression ?

When the wave is moving through air, the air is being compressed at the wave crest and the air is being rarefacted on the trough. 

 

Crests represent maximum amplitude of a wave, which is analogous to compression which represent maximum density regions.

 

Troughs represent minimum amplitude , which is analogous to rarefactions which are low density regions.

 

So, the comparision between crest/troughs and compression/rarefractions is made between the amplitude (intensity) to the density (pressure).