The term exercising options means performing the right to buy or sell the underlying asset at the strike price stated on the contract before the expiration date. The value of options rise and fall depending on the underlying stock's volatility. The constant fluctuation in price of options whether caused by time or or its intrinsic value means that the contracts themselves can be bought and sold at a profit or at a loss. However, if the ultimate purpose of the option holder is to purchase the stock before the contract expires, the holder is said to be exercising his options. When options are exercised, the option holder buys the stocks owned by the options writer at the strike price. For put options, the holder of the put exercises the option by assuming a short position starting at the strike price and buys back the stock to cover at a profit.
You may wonder why most traders would use options if their goal is to purchase the stock anyway, the reason is that they are using a relatively small amount of money to control a particular number of shares without risking more than they are willing to pay for the option. If they used limit orders instead, they are already commited to take losses should the stock go the opposite way because they already own the stock. Limit orders are only executed once the price stated by the client is met. For example, suppose Boeing is currently trading at $70 and a trader wants to take advantage of an upward momentum. The trader would place a limit order for Boeing at $71 hoping that the stock would go even higher to $75 and close the position. At 100 shares, it would cost her $7,100. If the stock goes higher, then its good for her but if the stock lost momentum and fell rapidly back to $66, she would have lost a total of $500. Now if she bought a call option instead, it would have saved her a lot of money. Suppose a $71 strike price for Boeing costs $1, it would only cost her $100 to buy a call option. If the stock goes higher to $75, she can just exercise her call option at the strike price of $71 and sell the stock at the current market price of $75 for a $400 profit. If the stock dropped down to $66 dollars, her capital is not fully exposed because she does not own the stock. At $66, she can just walk away from the contract and not exercise the call option, she only lost $100 which was the amount paid to buy the call option. That is way better than losing $400 more.
If a trader decides to exercise an option, he would have to notify his broker in advance. There are different rules on exercising options by region, American style options can be exercised at any time before its expiration date while European style options can only be exercised at expiration date.