Green’s Dictionary of Slang

(US campus) strong physical attraction.

1981		Eble Campus Sl. Mar. 3: MDG – [...] strong physical attraction usually excluding feelings of love and friendship: ‘On GH, Jeff and Diana had an MDG’.
1996		Eble Sl. and Sociability 37: Two kinds of shortening reduce words to letters. The dominant type in college slang is initialism, which names the individual letters: [...] MDG (mutual desire to grope) ‘strong physical attraction’.