In short, 4/4 means full color printing on both sides. The term "Four Over Four" is print lingo for 4 colors on one side, and 4 colors on the other side (both sides of the press sheet).
The number 4 represents the 4 colors that make up the CMYK color model in printing. Cyan, Magenta, Yellow and blacK (CMYK) is easy to understand. Remember when you were a kid in school and they gave you 3 primary colors to mix into other colors? Well the same principal is applied here (plus blacK) in tiny dots of ink making up the final printed graphic.
4/1 "Four Over One" is full color front side and black and white or grayscale on the back.
4/0 "Four Over Zero" means full color on the front but no printing on the back.