This was used to punch paper tape for sending high speed telegraph messages using the Wheatstone system.
The operator would have 2 hammers (one in each hand) to strike the 3 buttons to punch the message onto the tape.
Automatic Telegraph 1868
From the left, the clockwork receiver, the clockwork transmitter, with an independent key in front for short messages, and the tape punch.
Sending 120 words a minute between
A History of the Telegraph Companies in Britain between 1838 and 1868. By Steven Roberts.