Exercising an option means exercising your rights to buy or sell
the underlying asset in accordance to the parameters of the
option.
When you exercise a call option, you will get to buy the
underlying stock at the strike price no matter what price the stock
is trading at in the market.
When you exercise a put option, you will get to sell the
underlying stock at the strike price no matter what price the stock
is selling at in the market.
In both cases, the option you own disappears from your
account.