I never warmed to this phrase. It means a youthful time, accompanied by carefree idealism, though recently in the U.S. it also means when someone is at the peak of their abilities. People claim this makes sense because salads are fresh and wilt quickly.
Wikipedia says the phrase was coined by Shakespeare in 1606 in Antony and Cleopatra. Cleo says “My salad days, / When I was green in judgment, cold in blood.” There are many sites that agree: Shakespeare seems to make a reliable source.
The phrase became popular only from the middle of the 19th century and has had many literary uses. Phrases.org notes that “Salad Days” was the title of a popular British musical in 1954.
It still leaves me cold.