If I have sold the Call Option: it means the buyer of this option has the right to buy (the underlying) whenever he wants, if he wants.
If the price of the underlying in the local (cash) market is higher than the strike price (pre-agreed price), he will exercise his right to buy from me (using his Call Option); and I will have to sell to him at that lower price.
Example:
I have sold the call option:
Underlying: share of ABC
Strike price: INR 50
Price of the underlying in the local (cash) market is higher, say INR 60.
In this case, the buyer of this Option (Call Option) will exercise his option and buy at 50. I will have to sell at 50, even if the price I can fetch in the local (cash) market is 60.
On the other hand, if the price of the underlying in the cash market were INR 40: Will the other party (Option buyer) exercise his right here?
Yes, he will exercise his right and buy from me at INR 50.