Why A relay is a switch whose contacts are opened or closed by an electromagnet: current through the coil pulls an armature that moves the contacts. That lets a small control current (from a low-power circuit, a keying line, or a microcontroller) switch a much larger or completely isolated circuit, such as an antenna changeover or an amplifier's AC power. The coil and contacts are electrically separate, which also gives useful isolation between control and switched circuits.
Watch out The amplifier choices describe active devices like transistors; a relay has no gain and only makes or breaks a connection. A pass transistor is the series element in a voltage regulator, not a switch controlled by a coil.
Relay = coil pulls contacts. Small current in, big circuit switched. It switches, it does not amplify.