In the financial markets, participants trade (buy and sell) financial instruments. Simply put, these are legally binding contracts. Of these, some are non-standard and these can be hard to deal with, as one would need to read all of their terms in order to make knowledgeable decisions. The others are standardized. The latter ones are called securities.
Of the securities, some are primitive, like bonds and stocks. The more complex securities that are built on top the bonds and stocks are called derivatives. Due to this multilayer approach, derivatives always have an underlying asset. The most common assets are stocks and bonds, but they can be pretty much any other securities.
Options are also derivatives. An option is the right (but not the obligation) to trade (buy or sell) an underlying asset at a given time or during a given time period at a predetermined, agreed upon price. If the trading is buying, the option provides its owner the right to buy (aka call in) the underlying asset and is, therefore, known as a call option. Conversely, if the trading is selling, the option is a put option and confers its owner the right of selling (putting away) his underlying asset.
For a call option, if the underlying asset appreciates above the strike price, its owner can exercise it for a profit. In this situation we say that the option is in the money and the difference between the strike price and the current value of the underlying asset is the intrinsic value of the option.