"That is what I dig about."="That is what I like about you."? What context do we use "dig" instead of "like" in?
It's quite slangy. Also, I don't think very many people use "dig" in that sense anymore.
"Dig" used in that sense is slang for something that you enjoy or like or something that you would appreciate. (For example, my husband will occasionally say to me when we're both comfortably ensconced on the sofa in front of the TV "I could really dig a cup of coffee right now," which is my cue to get up and fire up the coffee maker.) "Dig" was used in that context much more during the 1960s and 70s, and some folks will identify those who still use it as "aging hippies," but it's not completely out of vogue.
Some other examples:
"Are you a U2 fan? I totally dig their first two albums!"
"I'm sooo hungry, I could really dig a Big Mac right now."