The forward rate and spot rate are different prices, or quotes, for different contracts. The forward rate is the settlement price of a forward contract, while the spot rate is the settlement price of a spot contract.
A spot contract is a contract that involves the purchase or sale of a commodity, security, or currency for immediate delivery and payment on the spot date, which is normally two business days after the trade date. The spot rate, or spot price, is the current price of the asset quoted for the immediate settlement of the spot contract. For example, say it's the month of August and a wholesale company wanted immediate delivery of orange juice, it will pay the spot price to the seller and have orange juice delivered within 2 days. However, if the company needs orange juice to be available at its stores in late December, but believes the commodity will be more expensive during this winter period due to a higher demand than supply, it cannot make a spot purchase for this commodity since the risk of spoilage is high. Since the commodity wouldn't be needed until December, a forward contract is a better fit for the investment.
Unlike a spot contract, a forward contract is a contract that involves an agreement of contract terms on the current date with the delivery and payment at a specified future date. Contrary to a spot rate, a forward rate is used to quote a financial transaction that takes place on a future date and is the settlement price of a forward contract. However, depending on the security being traded, the forward rate can be calculated using the spot rate.
For example, say a Chinese electronic manufacturer has a large order to be shipped to America in one year. The Chinese manufacturer engages in a currency forward and sells $20 million in exchange for Chinese yuan at a forward rate of $0.80 per Chinese yuan. Therefore, the Chinese electronic manufacturer is obligated to deliver 20 million dollars at the specified rate on the specified date, six months from the current date, regardless of fluctuating currency spot rates.
You might be thinking of how the forward rate is calculated. Investopedia's got you. Read How do I convert a spot rate to a forward rate?