A put option is a derivative. It is the short equivalent of a call option.
Shorting a stock is taking a position that the stock price will fall. For example, imagine stock XYZ trades at $20 per share. You believe the stock will fall. You decide to short 100 shares of the stock. You contact your broker, and the broker loans you 100 shares of XYZ stock. You immediately sell those shares at the $20 price, gaining $2,000. A week passes and XYZ falls to price of $15. You decide to close your short. You purchase 100 shares of XYZ in order to return the loan to your broker. The total cost is $1,500. Subtracting the cost of $1,500 from the $2,000 gain leaves you with a profit of $500.
A call option is the right to purchase 100 shares of a stock at the strike price on or before the maturity date. Conversely a put option is the right to sell 100 shares a stock at the strike price on or before the maturity date. In other words, the put option is a leveraged short position.
Consider stock XYZ again, with a price of $20. A put option at the $20 strike gives the buyer the right to sell XYZ at $20, while the option writer must buy XYZ at $20.
The put options with a $20 strike are at-the-money. This means the put option has no intrinsic value since the stock can be sold at the $20 strike. The option premium is entirely extrinsic value.
XYZ falls to a price of $15. The option buyer may purchase 100 shares at $15 for a cost of $1,500 and sell them to the option writer at $20 for a gain of $2,000. Subtracting the $1,500 cost from the $2,000 again leaves the option buyer with a profit of $500.
Just like a call option, put options are two sided contracts. There is a buyer and a seller (the seller is called the option writer). The buyer is taking a short position in the stock. The option writer is taking a long position in the stock.