It's slang for 'understand'.
"What school do you go to?"
" _______ school"
"Ohh I dig"
Sam: Joanna asked me to come round her house
John: Rah man, did you dig her
Sam: Yh man, ofc
Digging a hole in the ground really fast with your shoe
“Hey let’s just dig into Gotham instead of waiting in line”
To insult somebody while looking like complimenting somebody.
That fucker thought he was sly, but I knew he took a dig at me.