Investopedia article - good
Delta
rate of change of the option price w.r.t. the price of the underlying asset.
Delta tells us how much an option price will change given a one-point move of the underlying. But since Delta is not fixed and will increase or decrease at different rates, it needs its own measure, which is Gamma.
Gamma
rate of change of the option's delta w.r.t. the price of the underlying, when all else remains the same.
If gamma is small, delta only changes slowly and in order to keep a portfolio (a basket of shares and options) delta-neutral, adjustments to the portfolio can be made less frequently. If gamma is large, i.e. delta is very sensitive to the underlying price, the portfolio will need to be adjusted frequently to maintain delta-neutrality.
When the option is deep in or out of the money, gamma is small. When the option is near the money, gamma is largest.
Vega
Option value with respect to the volatility of the underlying.
The volatility is the average standard deviation over the past year.
E.g. an option traded at £100 with 20% volatility has been trading between £80 and £120.
Theta
Sensitivity to time. Value of an option decreases with time\ as it nears its expiry date.
As such, theta is nearly always negative for bought options. This makes sense because Time Decay erodes the option value as time to expiration diminishes.
During the last month of an option, as it approaches expiry, its value decays exponentially. Very bad.
Rho
Least important - to do with specifically stock option calls and interest rates. Weird one.