The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset.
Many day traders who trade futures, also trade options, either on the same markets or on different markets. Options are similar to futures, in that they are often based upon the same underlying instruments, and have similar contract specifications, but options are traded quite differently. Options are available on futures markets, on stock indexes, and on individual stocks, and can be traded on their own using various strategies, or they can be combined with futures contracts or stocks and used as a form of trade insurance.
The currency market, or foreign exchange market ("forex"), was created to facilitate the exchange of currency that becomes necessary as the result of foreign trade. That is, when an entity in one country sells something to an entity in another country, the seller earns that foreign currency. When China sells t-shirts to Walmart, for example, China earns US dollars. When Toyota wants to build a factory in the US, it needs dollars. It may get those from its local bank, which in turn will obtain them in the international currency market. This market exists to facilitate these types of exchanges.
When buying or selling options, the investor or trader has the right to exercise that option at any point up until the expiration date - so simply buying or selling an option doesn't mean you actually have to exercise it at the buy/sell point. Because of this system, options are considered derivative securities - which means their price is derived from something else (in this case, from the value of assets like the market, securities or other underlying instruments). For this reason, options are often considered less risky than stocks (if used correctly).