Faucet hoses connect the faucet stems under the sink to the water supply. The hoses are flexible, allowing the sink above to be situated according to your needs. The faucet hose is also called a faucet water supply line and there is one for the cold and one for the hot. These hoses connect your faucets to the water supply valves underneath the sink. They are connected to either a shut off for the hot and cold water pipes or to the pipes directly if there are no shut offs.