In contrast to a printed (hard-copy) manual, which you could read **off-line** (while not using a computer).
The term dates back (at least) to time-sharing systems. Users may have had a terminal which could be used for typing text, punching paper tapes. But they were only able to use the computer when they were **on-line** (the "line" referring to the communications link from the terminal to the computer).
Lots of English is that way: you likely use terms which on reflection you might not consider up-to-date.