of the day
1 : served in a restaurant as a special item on a particular day
▪ What's the fish/vegetable of the day? ▪ Our soup of the day [=du jour] is vegetable beef.
2 : of a particular period of time
▪ What were some of the popular movies of the day? [=that were popular during that time] ▪ the important issues of the day

Andy Rathbone started geeking around with computers in 1985 when he bought a 26-pound portable CP/M Kaypro 2X. Like other nerds of the day, he soon began plying with null-modem adapters, dialing computer bulletin boards, and working part-time at Radio Shack.

Does the day mean the mid-80s?

Yes, that's the idea. The era when nerds were starting to get interested in the early computers.

HUBLOTDoes of the day mean the mid-80s?
It is definition (2) - it means during this particular period of time, without giving any range of dates or years.