Put option and call options are two type of transactions taking place with respect to trading in stocks and commodities, which are collectively called options.
An option is a contract that gives the buyer (holder) of the option the right, but not the obligation, to sell an asset like a stock or a commodity at an agreed price and time in future from the seller (writer) of the option. In call option the purchaser of the option has the right to buy the agreed asset, from the seller of the option, at an agreed price and and time. The cost of the total transaction (for example 100 shares at a set price) is called option premium: "The amount per share that an option buyer pays to the seller."
In put option the seller (writer) of the option giver the seller (holder) of the option the right, but not the obligation, to sell to the writer an asset at agreed price and time. In this case also the cost of the total transaction is called the premium.
An option is a contract between two parties where one party gives the other a right but not an obligation to either buy or sell a particular asset at a pre-defined price that is mentioned in the option. The asset that can be bought or sold according to the terms of the option is called the underlying instrument and the price is called strike price.
Now, a put option is the right to sell the underlying instrument and a call option is the right to buy the underlying instrument. So if the person buying the option expects the price of the underlying instrument to fall he would buy a put option and if he expects the price of the underlying instrument to rise he would buy a call option.