What is Greeks?

Legal Definition
In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities, risk measures or hedge parameters.
-- Wikipedia
Legal Definition
RISK measures for DERIVATIVES that are used to determine the price sensitivity of contracts to changes in the UNDERLYING ASSET (DELTA, GAMMA), VOLATILITY (VEGA), passage of time (THETA), and INTEREST RATES (RHO). The greeks of individual contracts can be added to determine the sensitivities of an entire PORTFOLIO, allowing for efficient pricing and RISK MANAGEMENT. The general impact on the value of an option for a unit increase in the relevant variable is given as: Also known as OPTION SENSITIVITIES.