When you buy a call option, you give somebody money for them to have to deliver something for a price in the future, but where you don't have to take it if you change your mind. A put option is the same except you give someone money so they will be obliged to receive something for a price in the future. They say an option that you buy is "the right but not the obligation to buy or sell something at a fixed date in the future for a fixed price." An option that you sell is the obligation to fulfill that contract.

Why would someone do this? Well, say you will receive 2000 tons of gold next month because you found el dorado or something, but you don't have anywhere to put it. You can pay people today to receive gold at the current price next month, regardless of what the price is next month. If the price of gold goes up, you can just sell the gold you received for the market price, but if the price goes down, you can sell it for last month's price.

It's an insurance contract that dates back to Babylon. Farmers could negotiate a delivery price in summer for their harvest in the fall. That is, pay a little bit of gold in the summer to guarantee they could receive much more gold in the fall. Babylonian traders usually could then export the received goods at a higher price, so they were just looking for income on both ends of the trade.