The Gamma-Theta story

• Gamma and theta are usually of opposite signs and of similar magnitude. This comes from the fact that they are on the same side of the pricing PDE, and other terms are usually smaller in magnitude.
• Suppose you are a market-maker selling a call option. The option value decreases with time, does that mean you can just sit there with your premium? No, you have to delta-hedge the short call position. And due to convexity of call option price with respect to asset price (it is actually CONCAVE when you are shorting), you lose a small bit whenever you adjust your delta-hedge discretely. At the end of the day if volatility stays constant at the original implied level, your premium should exactly cover this hedging cost.
• Similar story can be told from the other side (the option buyer), who would get her premium back when she delta-hedges. It is in these senses that theta is considered a 'cost' to purchase gamma, and vice versa depending on the position you hold.
• Of course, if realized volatility turns out to be varying, somebody would get hurt. Delta-hedging of a vanilla option is a way to capture volatility changes, but it is not effective due to path dependence.
  

Reference: Veronesi, Wilmott "Paul Wilmott on Quantitative Finance" Ch. 12