A quanto (or cross-currency derivative) is a cash settled derivative (such as a future or option) that has an underlier denominated in one ("foreign") currency, but settles in another ("domestic") currency at a fixed exchange rate. For example, the Chicago Mercantile Exchange (CME) trades futures on Japan's Nikkei 225 stock index that settles for USD 5.00 for each JPY .01 of value in the Nikkei index. If you hold a future, and the Nikkei rises JPY 12 (or 12 points), you earn USD 6000.
Quantos are attractive because they shield the purchaser from exchange rate fluctuations. If a US investor were to invest directly in the Japanese stocks that comprise the Nikkei, he would be exposed to both fluctuations in the Nikkei index and fluctuations in the USD/JPY exchange rate. Essentially, a quanto has an embedded currency forward with a variable notional amount. It is that variable notional amount that give quantos their name—"quanto" is short for "quantity adjusting option."
Quanto options have both the strike price and underlier denominated in the foreign currency. At exercise, the value of the option is calculated as the option's intrinsic value in the foreign currency, which is then converted to the domestic currency at the fixed exchange rate.
A quanto swap (differential swap or diff swap) is a fixed-floating or floating-floating interest rate swap. One of the floating rates is a foreign interest rate, but it is applied to a notional amount in the domestic currency. For example, a US investor might make USD payments at 3-month USD Libor and receive USD payments at 3-month GBP Libor – 85, with both payments calculated by applying the respective interest rates to a USD 100MM notional amount. Floating-floating diff swaps are a vehicle for directly betting on spreads between different currency's interest rates.