Premium can be defined as per follow:

1.     Shares:     The difference between the higher prices paid for a fixed-income security and the security’s face amount at issue.
2.    Insurance: The specified amount of payment required periodically by an insurer to provide coverage under a given insurance plan for a defined period of time. The premium is paid by the insured party to the insurer, and primarily compensates the insurer for bearing the risk of a payout should the insurance agreement’s coverage be required.

Premium of an option is basically the sum of the option’s intrinsic and time value. It is important to note that volatility also affects the premium.

The amount by which a bond or stock sells above its par value.