In one line
An option is a contract that gives its holder the RIGHT to trade something at a fixed price on or before a fixed date, and gives its writer the matching OBLIGATION to take the other side if the holder uses that right.
How it works
Two words carry the whole idea. A CALL is the right to buy at the fixed price; a PUT is the right to sell at it. The fixed price is the strike, the fixed date is the expiry, and the money the holder pays the writer for the contract is the premium.
The asymmetry is the point. The holder chooses whether to use the right and never has to, so the most the holder can lose is the premium already paid. The writer has no choice — if the holder exercises, the writer takes the other side — so the writer collects the premium up front and carries the open-ended side of the contract afterwards.
On this desk the something is an index rather than a share. NIFTY, BANKNIFTY and SENSEX options settle in cash: nobody delivers fifty shares of anything, and the difference between the strike and where the index settled is paid across in rupees. That is why an index option can exist at all — an index is a number, not a thing anyone can hand over.
What it is not
An option is not a share of anything and it does not pay a dividend. It is a contract with a date on it, and after that date it does not exist. It is also not a smaller version of the underlying: two contracts on the same index with different strikes behave differently from each other, and one of them can lose its whole value on a session the index barely moves.