Out-Of-The-Money refers to an option that is unfavourable to exercise. An example is a put option with a strike price lower than the underlying stock price, or a call option with a strike price higher than the underlying stock price.
An Options Contract is a contract which specifies how much of the underlying asset can be bought or sold at a specific price. An option contract to buy the underlying is a call option, and to sell the underlying is a put option. Most stock options contracts represent 100 underlying shares.