The intrinsic value of an option is the value of the option if it is exercised today.
In the case of a call option, if the stock price is greater than the strike pricethen intrinsic value is the difference between the current price of the underlying stock and the strike price.
In the case of a put option, if the strike price is greater than the stock price then the intrinsic value is the difference between the strike price and the current price of the underlying stock.
The option is said to be in-the-money when the intrinsic value is large. In cases when the option id out-of-money meaning that the intrinsic value is negative, it is given as zero.