As I understand it, Telegraph/Telephone Block is control of the line between stations using telegraph, later telephone rather than block telegraph, or lock and block. In the case of a single line there was a precise procedure for offering and accepting trains, with everything being recorded in the block register - hence its alternative name 'Paper Block.' The dialogue would go something like:
A would phone B and say: 'Train Message. Do you accept Train 1234?'
If the line is clear B replies: 'Train 1234 - yes.'
This is repeated by Operator A and Operator B confirms that he has repeated the message correctly. The same sort of statement-repetition-confirmation process is repeated when the train leaves A, and when it reaches B, so that the two station operators are completely clear what is where. The Somerset and Dorset Joint did something similar using block instruments, but with their traffic summer density and sloppy operating practices they ended up having a rather spectacular head-on prang c.1876, which kind of put the first nail in that particular coffin in the UK.
On double lines the offering and acceptance of trains was omitted, but the train entering block, and leaving block messages were still transmitted, and the register kept. Of course, the safety of the whole system ultimately lay in the timetable which was 'the Law and the Prophets' so far as Paper/Telegraph Block was concerned.
I hope I am not doing too much violence to the concept. Please feel free to leap in.