Imagine I wrote on a piece of paper the following phrase:
I, Andy Novocin, will sell 100 shares of IBM to the holder of this piece of paper for a price of $50 USD each. This offer expires January 15th 2016
Assuming that I am a man of my word, how much is this piece of paper worth to you?
On March 19th 2015 IBM ended the day at a price of $159.81. So if you held this piece of paper (a call option with strike 50 and expiry: Jan 15 2016) you could immediately call me up, buy my shares at $50 and turn around and sell the shares at $159.81 apiece, for a profit of $109.81 per share ($10981 net profit).
So this piece of paper should sell for at least $10981 on March 19th, the value of an option that comes from merely using it (this is called exercising the option) is called the intrinsic value of the option.
But there is also something cool about being able to lock in this great purchase price for another 10 months, how much is that worth? That's a little bit harder to figure out.
This is called extrinsic value.