It is similar in form to a relay.
When a current flows through the induction coil, the resulting magnetic field attracts an armature that is held up against a metal arm. When the current is switched off, the armature is drops to its resting position, resulting in a "click". When the current returns, the armature is raised back to the upper arm resulting in a "clack." Thus, as the remote telegraph key makes and breaks a contact, the sounder echos the up and down state of the key.
Note that it is important that a sounder makes a sound both when the circuit is broken and when it is restored. This eases the process of identifying long and short presses of the key to send characters in morse code.
Note also that the default condition of the telegraph circuit is with electricity flowing. This enables the operator to easily detect a fault in the wire.