An option is a financial instrument that gives you the right to buy or sell shares at an agreed price at an agreed time in the future. The difference between options and futures is that the option does not carry an obligation to purchase or sell the shares, whereas a futures contract does. With an options contract the buyer may choose not to take up his right and let the option lapse.
The contract is struck between a seller and a buyer. The seller grants the buyer the option to buy or sell the shares at the agreed price and date. If the option is to buy shares then you purchase a call option, an option to sell shares is a put option.
Taking up the option is called exercising the contract. If the buyer chooses to exercise his option the seller is obliged to fulfil the terms of the contract. This shows that selling options carries more risk than buying them, as the buyer is the one who has the right to choose whether to exercise the option or not.
In return for granting the buyer this option the seller receives a payment called the premium. This will vary dependant on the time period of the option and the price at which the option is granted, called the strike price.
As far as the buyer's right to exercise the option is concerned, there are two main styles of option available. With an American style option exercise can be at any time before a set date in the future. With a European style option, it can only be exercised on a precise future date. Most over the counter options are European style, whilst those quoted on future exchanges tend to be American style.