Intrinsic value is the amount of profit an option would have if exercised immediately. It's only present when an option is in-the-money.
For a call option: Intrinsic Value = Stock Price - Strike Price (if positive, otherwise $0)
If Apple is at $150 and you own a $140 call, the intrinsic value is $10 per share, or $1,000 per contract.
For a put option: Intrinsic Value = Strike Price - Stock Price (if positive, otherwise $0)
If Apple is at $150 and you own a $160 put, the intrinsic value is $10 per share, or $1,000 per contract.
An out-of-the-money option has no intrinsic value. A $160 call on a $150 stock has zero intrinsic value because you wouldn't exercise it right now.
Option premium is split into two parts:
A $140 call on a $150 stock might cost $12. The $10 is intrinsic value, and the extra $2 is time value (the market's bet that the stock will move further).
Intrinsic value is guaranteed. If you exercise an in-the-money option, you lock in that profit. Time value decays as expiration approaches, but intrinsic value never changes (unless the stock moves).
Related: Extrinsic Value, ITM & OTM, Time Value