The "Greeks"

The "Greeks" are so called because they refer to five Greek letters - delta, theta, gamma, vega and rho - that are used to measure risk of an option.  An option is a financial instrument that is used for a variety of purposes, from protection of a stock or portfolio to generating income (please see Option Basics).  Options have a finite life, unlike the stocks the represent.  Because of this predetermined lifespan, options are considered risky instruments.  In truth, one ought to express this as options carry risk, rather than stating that they are risky, because in fact, options are not inherently risky.  But because they carry risk, that risk is measured by various factors, such as time to expiration, strike price, volatility, etc.

Calculations that measure risk are called Greeks.  These calculations were formulated and coined as the Greeks by three Nobel-prize winning academics, Fischer Black, Myron Scholes and Robert Merton.  For an exhaustive review of the Black-Scholes Model, please see http://www.investopedia.com/terms/b/blackscholes.asp.

In its short form, the Greeks calculate how an option price will change with the passage of time, change in the price of the underlying instrument, and other market conditions. 

Delta refers to the sensitivity or relationship of an options price relative to a $1 change in the price of the underlying instrument.  Delta is expressed from 0 to 100 for calls and from -0 to -100 for puts.  The delta value will change according to the strike price of an option, whether it is in the money (ITM) or out of the money (OTM).  Delta does not change at a uniform rate, because the underlying instrument does not change at a uniform rate.  For example, an option might have a strike price $10 below the current stock price, with an expiration one month hence.  However, the stock may remain very close to its current price for days, or even weeks, yet the option itself is a moving target by virtue of the passage of time.  Therefore, the delta (as well as the other Greeks used to measure its risk) will move and change over time.   Enter Gamma.

Gamma measures how delta will change based on a change in price of the underlying instrument. 

Theta measures how delta will change based on the time left to expiration.

Vega refers to how delta will respond to a change in volatility.

Rho refers to how much an option price changes relative to a change in interest rates. 

I have attempted to synthesize these definitions, but you may obtain additional information from https://www.thinkorswim.com/tos/displayPage.tos?webpage=lessonGreeks.