These are the precursor to QSL stamps etc. These are most often encountered by mistaken and beuddled postal stamp collectors.
Telegraph stamps are service fee stamps that prove payment for delivery of a telegraphic message. They are first cousins of postage stamps, which prepay a very similar service: delivery of a message through the postal system.
Initially postage or revenue stamps were used to indicate payment of the government telegraphy fee. (Yes a telegraph tax. why not, Syria taxed urination in Roman times... ) Over time, many governments began to issue separate telegraph stamps.
Sending a prepaid telegram was quite similar to posting a letter. The telegraph stamp was applied to a telegraph form containing the message to be sent and dropped into a telegraph collection box. Couriers emptied the boxes and took the forms to the servicing telegraph office from which the message was sent. At the receiving end, messengers delivered the telegram to the recipient. Literature on telegraph stamps is rare nd is limited to a few specialized catalogs listing telegraph stamps by their respective country of origin.
Stephen Hiscocks, an amazingly dedicated nerd compiled a book of them in 1982 called Telegraph and Telephone Stamps of the World.. It's a little hard to find as it was self-published...
But as Telegraph wires came down and wireless stations came up the telegraph stamp started to seem so quaint, and eventually they expired.