The plumbing fixture that an outdoor water hose is attached to is usually called a hose bibb, spigot or faucet. It may also be called a coupling, a connector or an adapter.
The spigot or faucet is where the hose is attached to the water source. It is used to control the flow of water from the source as it moves into the hose. Outdoor water hoses may also be connected to a nozzle at the end of the hose where the water exits the hose. The nozzle is used to control and direct the flow of water as it exits the hose.