Limited Risk and Unlimited Profitability to the Buyer:

A call option is bought when the contract buyer is bullish (expects that the price would rise) about the underlying asset and expects that a profit could be made by exercising his right (to buy) at the strike price and selling the asset at a higher price which is decided by the spot value of the asset. If things are going as expected, the call buyer can make a handsome profit and this could be termed as unlimited.

On the other side, his loss is limited only up to the premium paid if the value of the asset remained stagnant or even lower.

For example, person A purchases a right to buy 100 shares of Infosys Technologies at a price of Rs.3500 (strike price) per share on the last day of December,2001(expiry day) and the right is bought at a premium of Rs.100 per share. Also assume that Infosys share price has increased to Rs.3900 on the expiry day. The call buyer will purchase Infosys at Rs.3500/share(since this is the strike on the contract) from the call seller and the same will be sold at Rs.3900/share because it is the settlement value. His gain after deducting the premium is Rs.300 per share.

Conversely, suppose that value of Infosys has come down to Rs.3000 on the expiry day. He can simply walk away from the contract and what he has to lose is the premium and nothing more.