A stock option is an option to take up (otherwise known as "subscribe") to a share of a company at a pre-specified price. Most options have an expiry date. Option means the final decision whether to take up the share or not rests with you, the holder, there is no obligation to do so. For a listed company with a publicly-quoted stock price (on a stock exchange), the deciding factor whether to exercise an option or to let it expire worthless will be whether the subscription or exercise price is less than the market price ie. the price at which you can buy directly from the stock market. There are different terminologies for these situations, which are beyond the scope of this question at the moment.
When you say how useful is it, do you mean useful to the option holder or to the company which issued the option? There are several advantages to both the company and employees or investors. For instance, employees who are given options in listed companies will be motivated to ensure the success of the company so that it's share price will appreciate and their options will be worth more. Obviously higher staff productivity benefits the company as well. There are too many other advantages to be covered here. Hope this helps give you a basic understanding.