How Computer Hacking started
An IBM Mainframe
Computer hacking started as an "outgrowth" from "phone phreaking". The latter was the practice of, essentially, hacking the phone system. For example, getting long distance or even international calls at local call rates or even for free. It also involved being able to get at private phone calls, play around with company electronic switchboards and other mostly unsavoury games. Most such activities required a reasonable amount of technical knowledge of how the phone system worked and usually some electronic equipment, some of which had to be home built or at least adjusted - one could say "hacked".
Books on Hacking
A Friden Flexowriter - an early remote terminal!
The first computer systems that were hackable were those which had some kind of remote terminal (i.e. not in the big hall that housed the huge mainframe computer). These systems had rudimentary time-sharing facilities which were not always too secure. Although hacking attempts probably did occur in commercial installations, it wasn't until such computers started to be installed in universities that such hacking really got underway.
Things got more serious when terminals could be connected to the computer by a telephone line with a modem at each end. Now the phone phreaking community found that some of the numbers on their "unused/unlisted and therefore worth exploring" lists answered with a weird sound that was a bit like a fax machine but different. It didn't take anyone long to realise there was a computer at the other end of the phone line and try to connect to it - either from pure curiosity or to see if there was money to be made here.
Even getting started in this could be expensive as the teletype terminals needed for this weren't cheap. However, old telex machines could be (and were) converted in home workshops. Getting a modem was another matter as they were originally outrageously expensive. But even there the price eventually came down and amateur electronics magazines published projects for building your own. Equipment installed in universities and companies for perfectly legal use were also temporarily re-connected to be used for hacking. The rest, as the say, is history.
I'm sure there will be people who will give a different version of events but no-one knows the whole story - only what they encountered. And, of course, many of the original hackers are no longer with us. The use of the of the term "hacker" has changed in recent years: these days it is often used to refer to someone who creates or modifies software. However, when I first came across the term, in the context of a classified government communications project, that was not what it meant!