The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset. 
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When a trader buys an options contract (either a Call or a Put), they have the rights given by the contract, and for these rights, they pay an upfront fee to the trader selling the options contract. This fee is called the options premium, which varies from one options market to another, and also within the same options market depending upon when the premium is calculated. The option's premium is calculated using three main criteria, which are as follows:
Like futures markets, options markets can be traded in both directions (up or down). If a trader thinks that the market will go up, they will buy a Call option, and if they think that the market will go down, they will buy a Put option. There are also options strategies that involve buying both a Call and a Put, and in this case, the trader does not care which direction the market moves.
For example, if you bought a long call option (remember, a call option is a contract that gives you the right to buy shares later on) for 100 shares of Microsoft stock at $110 per share for December 1, you would have the right to buy 100 shares of that stock at $110 per share regardless of if the stock price changed or not by December 1. For this long call option, you would be expecting the price of Microsoft to increase, thereby letting you reap the profits when you are able to buy it at a cheaper cost than its market value. However, if you decide not to exercise that right to buy the shares, you would only be losing the premium you paid for the option since you aren't obligated to buy any shares. 
To reiterate, buying options in times of low volatility could prove to be advantageous should the volatility increase sharply. On the other hand, a lack of deviation in the price of the underlying asset will produce lower market volatility and even cheaper option premiums. Once again, pricing is relative and dynamic; "cheap" doesn't mean that it can't get "cheaper".
An option is a contract that allows (but doesn't require) an investor to buy or sell an underlying instrument like a security, ETF or even index at a predetermined price over a certain period of time. Buying and selling options is done on the options market, which trades contracts based on securities. Buying an option that allows you to buy shares at a later time is called a "call option," whereas buying an option that allows you to sell shares at a later time is called a "put option."