To short a stock is to sell stock one does not own.

Security holdings are known as “positions”. A “long” position means one has bought the security. If you are long and then sell it, that is called “selling long.”

If you do not own the security, but sell it to someone, you are “short”

Short selling is permitted because it carries an implied future demand to buy the stock. The seller can borrow stock to deliver to the buyer. Then, when the price has dropped, one covers the short position by buying the stock at a lower price than where it was sold. The difference is the profit from short selling.

You think stock X will go down.
You borrow a share of X at $1
You sell it at $1
You are correct, it goes down to $.50
You buy it back at $.50
You return the stock to the original owner.
You made $.50

You are betting a stock will lose money.
After 9/11, several people were investigated when it was discovered they had shorted several airline stocks.
The movie The Big Short explains this pretty well.

@josie got the mechanics right. A few things to add. You have to pay for the right to borrow the stocks. Why else would someone lend you their stock? Selling short is risky. The most you can make is the current value of the stock, if it goes down to zero. There is no upper bound to what you can lose, since there is no bound to how much the price can go up.

A less risky way of betting that the price of a stock will go down is to purchase a put option. This allows, but does not require, the option buyer to force the sale of the stock to the option seller at a specified price by a certain date. If the stock price goes below the specified price, the value of the option goes up. If the value of the stock goes above the specified price, the option is worthless, but the most you can lose is the cost of the option.