"Old Time" is used to describe the world pre-nuclear disaster in two Harry Turtledove works. While Turtledove probably did not intend for both stories to be set in the same continuity, the references to the Old Time are similar enough to be both included here for convenience.
Old Time in "Secret Names"
Old Time referred to the civilization that existed prior to the global disaster of the Big Oops. The men of the Old Time were well known for their godlike powers and godlike goodness so it was a mystery why the locks on the ruins of their buildings were so much stronger than those of Madyu's day.
Old Time in The Valley-Westside War
Old Time referred to the civilization that existed prior to the nuclear war between the United States and the Soviet Union in 1967. Survivors in the former territory of the US, now split up into countless mini-states and chaotic lawless areas, had some idea about many of the Old Time's technological achievements such as electricity or automatic rifles, but no means of reproducing them. Surviving books from the Old Time had to be divided between "real" and "unreal" - i.e. those which described the world of the Old Time as it really was, and those which were fiction even in that time. Ordinary people in the late 21st Century sometimes found it difficult to distinguish the two and asked the advice of scholars. Even so, there was a great deal of conflation between fact and fiction. For example, the historical person Annie Oakley was conflated with comic strip character Little Orphan Annie, and was believed to be in league with Jesse James. Most people agreed that The Lord of the Rings was unreal, but it was beloved nonetheless.
The formula for preparing Coca-Cola, a drink known to have been widespread in the Old Time, was lost in the 1967 war and no one could really imagine what the drink tasted like - until Dan of The Valley uncovered the secret hoard of Coca-Cola cans from the home timeline in the basement of the Mendozas' house.