Intrinsic value is the actual, tangible value an option has if it were exercised immediately. It represents the difference between the option's strike price and the current market price of the underlying asset — but only when that difference is in the option holder's favor.
For call options, intrinsic value exists when the stock price is above the strike price. For example, if the stock is trading at $60 and the strike price is $50, the intrinsic value is $10.
For put options, intrinsic value exists when the stock price is below the strike price. If the stock is at $40 and the strike is $50, the intrinsic value is $10.
If an option is out-of-the-money, it has no intrinsic value — it is composed entirely of extrinsic (time) value.