expression
a long time ago; in those days
A set phrase used adverbially to refer to a distant past, often at the beginning of a story or reminiscence. Slightly literary or nostalgic in tone.
その昔、この村には大きな城があった。
A long time ago, there was a big castle in this village.
その昔は、携帯電話なんてなかった。
In those days, there were no mobile phones.
昔 is a general noun meaning 'old times' or 'long ago', while その昔 is a fixed phrase that specifically points to a particular distant past, often used in storytelling.
大昔 means 'ancient times' or 'great antiquity', implying a much more remote past than その昔.
Combination of その (that) and 昔 (old times, long ago). The phrase literally means 'that old time' and has been used since classical Japanese to refer to a distant past.