An option buyer is clearly someone who buys an option. He/she has the right to exercise it but not the obligation. An options buyer risks the loss of the premium if at the end discovers that it is pointless to exercise it.
An option writer is someone who sells the option but without having already a long position. It is like short selling in stocks. A writer has the obligation to keep the agreement if the option is exercised against him/her.
A writer and a seller is not the same, even if in options lingo these two words sometimes are used to denote the same thing. A seller is someone that has already bought an option and they sell it to close the position, whereas a writer is short selling an option and opens a new short position.
The writer of a naked call option has unlimited upside risk and the writer of a put has great risk to the downside, until the price of the underline goes to zero. He/she writes options in order to earn the premium.
When long in a put you win from the price decline of the underline asset but when short you are losing because of this decline.
Imagine that you have bought a call to buy 100 shares of MSFT at the predefined price of $25 after three months. You have paid $1/share to own this right. If the stock in three months is at $30 then you are exercising the right to buy it at $25 and you can sell it instantly at $30. Your revenue is $5/share, minus $1/share you paid for the premium and you have a profit of $4/share (minus commissions). If the price of MSFT after three months is at $20 you have no interest to exercise the call because you can buy the 100 stocks cheaper at market prices and in this case you will lose the $1 premium you paid.
But what happens to the writer of the same option? When MSFT after three months is at $30 he/she has the obligation to sell 100 shares to you at $25. If he hadn’t bought the stock already, he would have to buy it at market the price of $30 and sell it to you at $25 for a loss of $5. He has also earned from you the $1 premium so his net loss is $4/share (plus commissions). In case the stock after three months is at $20 the buyer will not exercise the call so the writer will have a net profit of $1/share which is the premium he earned.