Single Valve Faucet
As the handle is turned, the valve turns as well and allows cold water to flow past the valve and out of the faucet. When turned more, hot water is able to move past the valve as well and mixes with the cold. When the handle is turned as far as it will go, the valve closes off the cold water line again but leaves the hot water line wide open to let only hot water reach the faucet's spigot.
Dual Valve Faucet
A dual valve faucet is more common than a single valve faucet in kitchens, consisting of two separate valves which are controlled by different handles. The cold water line runs to one valve, while the hot water line runs to another. Each valve can be opened independently to allow hot or cold water to run through the faucet's spigot in the exact amount that you wish. This allows for a greater degree of temperature and pressure control than would be possible with a single valve.
Dual Spigot Faucet
Though not common in kitchen sinks, a dual-spigot faucet does exist and is preferred by some homeowners. This faucet is essentially a dual-valve faucet with the added feature of each valve being connected to a spigot of its own so that there is a complete separation of hot and cold water. Both spigots drain into a single sink, allowing the hot and cold water to be mixed to produce varying degrees of warmth as desired.