With options markets, as with futures markets, long and short refer to the buying and selling of one or more contracts, but unlike futures markets, they do not refer to the direction of the trade. For example, if a futures trade is entered by buying a contract, the trade is a long trade, and the trader wants the price to go up, but with options, a trade can be entered by buying a Put contract, and is still a long trade, even though the trader wants the price to go down. The following chart may help explain this further:

A sampling of terms defined includes: active premium, aggregation, angel financing, asset allocation, backwardation, benchmark, bridge loan, capital structure arbitrage, coefficient of determination, commodity option, convertible arbitrage, deferred futures, discretionary trading, distressed debt, enumerated agricultural commodities, extrinsic value, follow-on funding, hedge ratio, interdelivery spread, long short equity, modified value-at-risk, offshore fund, piggyback registration, social entrepreneurship, systematic trading, tracking error, underlying futures contract, venture capital method, and weather premium.

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). 
* Sell orders are subject to an activity assessment fee (from $0.01 to $0.03 per $1,000 of principal). Trades are limited to online domestic equities and options and must be used within two years. Options trades are limited to 20 contracts per trade. Offer valid for new and existing Fidelity customers opening or adding net new assets to an eligible Fidelity IRA or brokerage account. Deposits of $50,000-$99,999 will receive 300 free trades, and deposits of $100,000 or more will receive 500 free trades. Account balance of $50,000 of net new assets must be maintained for at least nine months; otherwise, normal commission schedule rates may be retroactively applied to any free trade executions. See Fidelity.com/ATP500free for further details and full offer terms. Fidelity reserves the right to modify these terms and conditions or terminate this offer at any time. Other terms and conditions, or eligibility criteria may apply.
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).