 Future and options are derivative products of any underlying.
 The term “derivatives” is used to refer to financial instruments which derive their value from some underlying assets.
 The underlying assets could be equities (shares), debt (bonds, Tbills, and notes), currencies, and even indices of these various assets, such as the Nifty 50 Index.
 Derivatives derive their names from their respective underlying asset. Thus if a derivative’s underlying asset is equity, it is called equity derivative and so on.
The main purpose of
derivatives is to transfer the price risk from one party to another; Risk is
transferred to those who are willing to take it.
For example, A rice farmer spends money and
effort in procuring land, buying seeds , manure , is dependent on water supply
and many other factors to produce rice.
If he spends Rs 20 per kg in producing rice ,
he obviously wants to sell his produce at a price higher than Rs 20 per kg.
But what if after 3 months (when finally
produce will be out) price of rice is less than Rs 20/ kg ?
So today, for protection, farmer may wish to
sell his harvest at a future date for a predetermined fixed price (more than
Rs 20 per kg) to eliminate the risk of change in prices by that date.
He enters into a contract for selling his
produce at Rs 24 per kg, 3 months from now. Such a transaction is an example of
a derivatives contract. The price of this derivative is driven by the spot
price of rice which is the "underlying".
1. Futures
2. Options
…
hence the term F & O.
Important point for futures and options :

They are traded in fixed lot sizes, size fixed by
exchange. Eg Lot size for Nifty is 75 units for both futures as well as
options of Nifty , Lot size for Banknifty is 30 , Lot size for Reliance
industries is 500.

Lot size is
same for an underlying, for future as well as option.

Options are traded at different strike prices. Eg If
Nifty is at 7000 , we will have options of 6900, 6950, 7000 , 7050 , 7100, …
and so on. So gap between different strike prices is of 50 points for Nifty.
For a stock which is in the range of Rs 1000, generally the gap is 20 points.
So for reliance the strike prices are
1000 , 1020 , 1040 and so on.

Expiry is on
same day i.e. last Thursday of month., which means after last Thursday of the
month, contracts for current month will not exist and all the settlements will
be done at closing prices on last Thursday.

Last Thursday is expiry day only for current month
contracts. But contracts for next month, 3^{rd} month and other quarter
end months will continue to exist.