Each future and option contract has an expiry date - last thursday of a each month. For example, the expiry for this month is 29th July 2010, for next month it is 26th Aug 2010.
In case of a future contract, if you buy one lot for say Reliance with Expiry date 29th July 2010, the lot would automatically be sold on the expiry date by the exchange - whatever the price may be. You can't hold that lot in the subsequent month. However, if you want to hold the contract till August, you can buy the next month's contract right now. Usually the price of a future contract is near about the spot price (a little higher or a little lower or may be even the same), and generally the price difference between the spot price and the future lot price is reduced around the expiry time.
My knowledge about the options is very limited, somebody else may be able to comment on that.