Perfectly elastic demand exists, at least in theory, in markets that are in the state of perfect competition. When demand for a product is perfectly elastic, the quantity demanded will change infinitely whenever the price changes at all. In other words, if you raise your price at all, you lose all your customers. Let us see why this would happen.
In order for this to happen, there have to be a large number of suppliers and all of those suppliers have to be selling the exact same product. First, this means that there cannot be any way to differentiate your product from someone else’s product. For example, imagine that you are all selling a certain type of wheat. All wheat of that particular type is essentially identical. Because all the wheat is identical, there is no reason for anyone to prefer your wheat to the wheat that someone else grows. Therefore, they will not pay any extra for your wheat. Furthermore, this means that there are many sellers. If you raise your prices, buyers can easily find someone else who will sell them wheat.
In this situation, there is no way for you to raise your prices. If you do, people will simply buy wheat from someone else. This is why the demand curve is horizontal. At the equilibrium price, you can sell as much wheat or as little wheat as you like. However, if you raise your price, you will not sell any wheat at all.
(In this market type, you are making zero economic profit. Therefore, you cannot lower your price because you will no longer be making enough money to stay in business.)