The fee you are paying to buy the call option is called the premium (it's essentially the cost of buying the contract which will allow you to eventually buy the stock or security). In this sense, the premium of the call option is sort of like a down-payment like you would place on a house or car. When purchasing a call option, you agree with the seller on a strike price and are given the option to buy the security at a predetermined price (which doesn't change until the contract expires).
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).