DTG (or Direct-to-Garment) printing is a unique type of printing that sprays the ink onto the garment, then the inks soaks into the fibers of the garment. It's like how paper is printed on, but with clothes.
This method of printing is useful for designs with many colors. Screen printing is charged on a per-design-color basis whereas DTG is not. So basically, if you're going to have over 8 colors in a design, it would be most cost effective for you to have the design DTG printed.