Delta — directional exposure
Delta is the sensitivity of an option's price to a $1 move in the underlying. Long calls have positive delta (0 to 1); long puts have negative delta (-1 to 0).
Gamma — curvature
Gamma is the rate of change of delta with respect to the underlying. It peaks at-the-money and is what makes short-dated options dangerous to short.
Theta — time decay
Theta is the daily bleed from time decay. It accelerates in the last 30 days. Theta-positive books (short premium) profit in calm, range-bound markets.
Vega — vol sensitivity
Vega is the sensitivity to a 1-point move in implied volatility. Long-vega books lose money in vol crushes even when direction is correct.