An option is a contract that represents control over 100 shares of stock ("the underlying").
A call option gives the holder the right (but not the obligation) to buy shares of the underlying at an agreed-upon price. If you think the price of a stock is going to go up, you would buy call options that give you the right to buy the stock at a lower price than it's currently trading.
A put option gives the holder the right (but not the obligation) to sell shares of the underlying at an agreed upon price. If you think the price of a stock is going to go down, you would buy put options that give you the right to sell the stock at a higher price than it's currently trading.