Extrinsic value (also called time value) is a little harder to understand. It's not something inherent in the option as it depends on a number of variables (time to expiration, strike price, perceived volatility). It is defined to be the premium a rational investor would pay over the intrinsic value based on the probability it will increase in value before expiration.
This concept is quite hard to put in words and you might not fully understand it unless you see it in real life. But there are a few things I could tell you that might help you grasp the definition.
At the time of expiration, all extrinsic value goes to zero, since at expiration the option is worth its intrinsic value. If the option lands ITM (in-the-money) then it is worth something, but if it lands OTM (out-of-the-money) then it is worth nothing. There is no more time value left in the option.
Here is a graph that depicts the price of a 100 call option (depending on the underlying value) across different times.
There are two things to notice:
First, the value of the option is higher when there is more time to expiration. If you have a call option OTM by a little bit (e.g. $7 call when the underlying is worth $6), whatever that call option is worth to you 1 week from expiration (say $1), it would be worth much less a few minutes from expiration (maybe $0.05). Why? Because a lot can happen in a week but only so much can happen in a few minutes and it is in that expectation your time value decreases.
Second, the closer the strike price is to the underlying value, the higher the extrinsic value. In the graph above, the extrinsic values are the differences between the given line and the line at expiration. Graphing just the extrinsic values gives us the following:
So, with that, let's look at a few examples.
The underlying asset is trading at $7. The $8 call option just traded for $1.10. What is the extrinsic value?
Since we know an option value is just the summation of its extrinsic and intrinsic value. What is its intrinsic value? Well, a $8 call (with underlying at $7) is intrinsically worth nothing. That is, it is OTM. So, then ExtrinsicValue = $1.10 - $0.00 = $1.10.
Underlying is trading $34 and the $30 call just traded for $7.75. What is the extrinsic value for this call?
Again, what is the intrinsic value. Well, the call is ITM by $4. So, $7.75 - $4 = $3.75.
Let's try this for a put. Underlying is $101. $95 put option just trades for $6.50. What is the extrinsic value?
Well, the put has an intrinsic value of $6 ($101 - $95). So, the extrinsic value of $0.50.
This idea of extrinsic value will be further explored when we talk about the decaying time value of an option (theta). We might not explicitly call it out as an extrinsic value, but remember an intrinsic value of an option does not change in respect to time (only by changing the price of the underlying).