Options are a contract between two parties to buy/sell an asset (in the future) using a fixed price and date. At that future date, the option buyer has the choice whether to continue with the buy/sale; the seller does not.
Options are (usually) either Call or Put options.
Call Option: the right, but not the obligation, to buy an asset in the future.
Put Option: the right, but not the obligation, to sell an asset in the future.
The economic pin that this all revolves around is the premium. This is the fee paid by the buyer of the option to the seller of the option.
The buyer will always pay and the seller will always receive the premium, regardless how the option settles.
Trad-Fi has two major styles of options: American and European.
Both styles are similar, the key difference is the window in which the buyer may exercise the option.