Compressibilty is a process of compressing matter,as solids cannot be compressed but gas can and liquids can be compressed to some extent
only gas is compressable fully 
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Compression is the process where we apply force to change the volume of the given object. this process us used by us a lot in our day to day like the CNG or LPG cylinders. Here in these cylinders we compress the gas content for easy usage and transport. hence we can understand that the compressibility is really helpful to us.