The dim time was a period in the history of Gamma Trianguli VI.

During this time, Akuta was outfitted with antennae, which he called "my ears for Vaal", as they enabled him to communicate with the "god". He related this fact in 2267 when Spock pointed out the antennae to James T. Kirk. (TOS: "The Apple")

This is the only reference made by the natives in the episode to the time in which Vaal was created, or in which their system of society was set up.