The expssion "writing an option" refers to the act of selling an option. An option is the right, but not the obligation, to buy or sell a particular trading instrument at a specified price, on or before its expiration.
When someone writes (or "sells") an option, he or she must deliver to the buyer a specified number of shares if the option is excercised The writer has an obligation to perform a duty while the buyer has the option to take action. There are two general types of option writing: covered and naked.
In a covered call, the option writer already owns the underlying trading instrument and wishes to make extra money from the position. He or she can write (or sell) an option based on the expectation that the underlying's price will move in a particular way. The buyer pays the writer a pmium in exchange for writing the option.
If the option trades at a value that benefits the buyer, the seller is obligated to hand over the shares. If the option expires at a value that does not benefit the buyer, the seller retains the original shares. If the option writer does not own the underlying instrument, it is said to be a "naked" option. This is more risky than writing a covered call since the writer is still obligated to produce the specified number of shares of the particular contract (without already owning them).