Here's how the connection works:
* "Dig" as a place to live: The word "dig" has been used colloquially to refer to a dwelling or residence, often in a modest or makeshift sense. This usage likely comes from the act of digging a hole or creating a space in the ground to live.
* "New digs" as a new place to live: When someone moves to a new place, particularly a new home, the phrase "new digs" is used to signify their new residence. The word "new" emphasizes the change in dwelling, while "digs" maintains the informal, sometimes slightly humorous tone.
The exact origin of the phrase is unclear and possibly has roots in multiple historical uses of the word "dig". However, the association with a place to live and the informal nature of the word contribute to its common use in modern English.