Quantity-Adjusting Option - Quanto Option
  
A quanto option works the same as a regular option. The only difference is that it operates across two different currencies. The pay off comes in a different currency than the currency used for the option's strike price and the underlying asset's trading price.
Let's break that down a bit. An option gives you the right to buy or sell (depending on the type of option) some underlying asset. So...you might hold an option to buy 100 shares of MSFT at $135, expiring in two months. MSFT in this case would count as the underlying asset. Fast-forward two months. It's expiration time. MSFT is trading at $145, meaning the option with the $135 strike price is in the money. You are going to exercise the option, buy 100 shares of MSFT at $135 and immediately sell them for $145, pocketing $10 a share...or $1,000 total.
So just to review: in this scenario, MSFT is valued in dollars. The strike price is listed in dollars.
A quanto option pays off in some other currency. When the option is purchased, an exchange rate is fixed, so that the quanto returns an amount in the other currency.
You bought your quanto option to pay off in euros. The EUR/USD rate was fixed at 1.15. Since then, the exchange rate has moved a little and is now trading at 1.10. However, you get the locked-in rate of 1.15. When you cash in your quanto option, the $1,000 return becomes €1,150.