In investing parlance, calls and puts are contracts that give you the right to buy or sell an asset at a specified price at some point in the future. The assets underlying the options are most commonly shares of stock.
A call option gives you the right to buy shares of stock for a set price, known as the strike price. If the share price rises higher than the strike price, you can make a profit by buying stock at the strike price and reselling it at the higher market rate.
A put option gives you the right to sell shares at the strike price. If the share price falls below the strike price, you can profit by buying shares at the market rate, then selling them at the higher strike price.
Options are just that--optional. They give you the right to buy or sell stock at a given price, but you are under no obligation to do so.
Options are bought and sold on options exchanges. The price you pay for an option is called the premium.
Long and Short
The buyer of an option--either call or put--is said to be in a long position. The seller is said to be in a short position.