How is hedging exchange rate exposure using options different from hedging using forward contracts?
Foreign currency positions that are taken can be hedged using options as well as forward contracts.
An option is an instrument that gives you a right but not the obligation to exercise it on expiry. For example if you are going to receive $1000 after a month and would like to sell it to buy Euros you can buy an option to sell $1000 dollars in return for Euros after a month at an exchange rate that is fixed when the option is bought. After a month you could exercise the right given by the option to sell $1000 in return for Euros if the transaction is profitable. But if the exchange rates are such that you make a loss by selling dollars at the rate that is specified in the option contract you don't have to exercise the right. If a similar position was hedged using forward contracts, you would have been obliged to sell $1000 for Euros at the end of the month irrespective of whether the exchange rates made the transaction profitable or a loss making one.
This flexibility that the use of options offers requires the payment of an amount called premium when the option is bought to the party that is selling it.