Phreakers were/are telephone system hackers. Back in the day it was possible to hack telephone systems using simple electronics and some technical knowledge. The page being linked to seems to go into some of the history of phone phreaking.

Incidentally, the following clip contains the most impressive demonstration of phreaking I've ever seen, showing a blind phreaker with perfect pitch called Joe Engressia who was able to hack the phone system just by whistling:

https://www.youtube.com/watch?v=vVZm7I1CTBs

A fair amount of the hacker culture of the 80s and early 90s (hacker in terms of what the common perception of a hacker is) seems to owe its debt to the trail blazed by phreakers.

My understanding is that this guy was a telephone "phreaker" (hacker enthusiast) and I gather he traveled a lot and would use pay phones and record them as he did.

The "tapes" are him narrating over these old tapes many years later explaining what he was doing. Much of it is him dialing various numbers and listening to the beeps/boops/kachunks and explaining exactly what is happening technically to route the call.