Call Option
  
A type of option that gives the buyer the right to purchase something for a set price for a predetermined, finite period. A call represents a bet that the underlying asset (the thing you have the right to buy) will see its price increase.
So say you like shares of Hopefully Going Up Co., which are currently trading at $20 per share. You might buy a call option with a strike price of $25 per share and an expiration one month from now. If a month from now, the stock has risen to $30 per share, you can exercise your option, buy shares at $25 per share, immediately sell them at the going rate of $30 per share and pocket the $5 per-share profit (minus whatever it cost you to purchase the call in the first place).
If shares of Hopefully Going Up Co. sink to $18 per share, you can just let your call option expire. You aren't required to buy the stock. Using call options lets traders make bets without forcing them to buy the underlying asset outright. This lowers the expense of placing the bet, and thus lowers the risk.
The opposite of a call option is a put option. A put gives the right to sell an asset at a certain price during a set period of time. It's a bet that the price of the underlying asset will go down, a way to short the asset.