Intrinsic value is a term commonly used when discussing options and other derivatives. The price of an option is made up of a combination of intrinsic and extrinsic value (commonly called 'time value').
Intrinsic Value - is the portion of the price based on value of the underlying investment. Options will only have intrinsic value when they are 'in the money'. For a call option this only happens once the market price has exceeded the strike price. Intrinsic value can be thought of as the 'asset backed value'
Extrinsic or time value - is the portion of the options price based on perceived value. There are several factors which make up time value, which are known as 'The Greeks'
If the market price of a share is $104, and a call option with a strike price of $100 is trading at $6, then this option has $4 of intrinsic value (actual gain from buying a $104 stock for $100), an $2 of time value.
At expiry, options will only have intrinsic value, if an option expires 'out of the money' then it will expire worthless