Basic Points

• Intrinsic value in options refers to what an option would be worth without any of its time premium (extrinsic value from what the options market is adding to its base and minimum value). 
• An option only has intrinsic value if it is ITM (in the money) because intrinsic value is entirely based on how much better the spot price is than the strike price. An option is ITM if it would still have some value if expiring with the underlying at its current price level. 
• On a risk chart, intrinsic value is shown as the sharp and jagged lines, but it represents the profitability of an option upon expiration or a situation with near-zero implied volatility (the expected percentage range over the next year based on option prices and with 68.3% confidence).

Advanced: Dynamics

When option traders say that they are focusing on trading intrinsic value, what they mean is they are focusing on trades which are ITM. To buy options which are ITM is to have the advantage of the defensive edge of gamma (the acceleration of directional exposure). What this means is how—when the price moves adversely against the position—that gamma will slow down the amount of damage done between point moves in the underlying security because gamma will be making delta smaller. 

<Credit Iron Butterfly risk chart retrieved from OptionsPlay>

Long ITM options are also generally more durable against options premium loss; this includes more resilience against time decay and IV crush (strong decreases in implied volatility which materially lower option prices). Part of the price paid for that durability is a higher premium, and less convexity (the nonlinear payout effects from gamma), which is the offensive power of gamma that will grow deltas (directional exposure) explosively when suddenly right about direction.