Definition
Intrinsic value is the amount of an option's price that would be realized if it were exercised immediately. For a call, it is how far the underlying's price sits above the strike; for a put, how far the price sits below the strike. An option that is not in the money has zero intrinsic value.
The remainder of the premium — anything paid above intrinsic value — is time value, the market's price for the chance that the option becomes more valuable before expiration.
Why it matters
How it works
Suppose a stock trades at 110 and a call has a 100 strike. The call has 10 of intrinsic value, because exercising it lets the holder buy at 100 and sell at 110. If the same call trades for 14, the extra 4 is time value. A put with a 120 strike on that same stock would have 10 of intrinsic value, since exercising lets the holder sell at 120.
As expiration approaches, time value bleeds away while intrinsic value holds steady, so the gap between premium and intrinsic value narrows. By expiration the two converge: a deeply in-the-money option is worth almost exactly its intrinsic value, and an out-of-the-money one is worth nothing.