Extrinsic value is what you pay for possibility. It is highest for at-the-money options with lots of time and high implied-volatility, and it decays to zero at expiration through theta.
Option sellers are in the business of collecting extrinsic value; option buyers are paying it and need the stock to move enough to overcome it.
Example: a stock is $100. A $100 call with 45 days left trades at $4.50. Its intrinsic value is $0, so all $4.50 is extrinsic. If the stock is still $100 at expiration, that $4.50 goes to zero.
Related: intrinsic-value, theta, implied-volatility, iv-crush