Call options give the buyer the right, but not the obligation, to purchase an underlying asset. They are available in various strike prices depending on the current market price of the underlying instrument. Expiration dates can vary from one month out to more than a year (LEAPS). Depending on the market, you may choose to buy (go long) or sell (go short) a call option.
If you choose to buy or go long a call option, you are purchasing the right to buy the underlying instrument at whatever strike price you choose until the expiration date. The premium of a long call option shows up as a debit in your trading account. The premium amount represents the maximum risk a long call strategy can incur. Profit is made on a long call when the price of the underlying asset rises above the strike price of the call. You can then either exercise the call or offset it by selling a call with the same strike price and expiration date.
By exercising a long call, you end up with 100 shares per option of the underlying stock at the call strike price. You can then turn around and sell the underlying asset at the current (higher) price to garner a profit on the difference between two (current price - strike price = profit). If you choose to offset the call option, the maximum profit is unlimited. The call's premium will increase in value depending on how high the underlying instrument rises in price beyond the strike price of the call. As the price of the underlying asset rises, the long call becomes more valuable because it gives you (or the person you sell it to) the right to buy the underlying stock at the lower strike price of the call.
If you choose to sell or go short a call option, you are selling the right to buy the underlying instrument at a particular strike price to an option holder. Selling a call option prompts the deposit of a credit in your trading account in the amount of the call's premium. You get to keep this credit if the option expires worthless. To make money on a short call, the price of the underlying asset must stay below the call's strike price. If the price of the underlying asset rises above the short call strike price, it will be assigned to an option holder who may choose to exercise it. This gives the option holder the right to buy 100 shares (per option) of the underlying stock from the assigned option buyer at the strike price of the short call. This means that the option seller must buy the underlying asset at the current price and sell it at the call's lower strike price to the assigned option holder, thereby incurring a loss on the trade (current price - strike price = loss). The maximum loss is therefore unlimited to the upside, which is why selling "naked" or unprotected call options comes with such a high risk. To offset a short call, you have to buy a call with the same strike price to close out the position.
Call options give you the right to buy something at a specific price for a specific time period. If the current market price is more than the strike price, the call option is in-the-money (ITM). If the current market price is less than the strike price, the call option is out-of-the-money (OTM). If the current market price is the same as (or close to) the strike price, the call option is called at-the-money (ATM).