It's literally the new version of a traditional tattoo. Take a traditional tattoo and increase the detail, decrease the line weight, modernize the use of color and add vivid highlights. By using varied colors and line sizes, you can create an exaggerated interpretation of the traditional tattoo.
Back in the late 70s, American folk art and pop culture were inspiring a new generation of tattoo artists in New York City. Their revolutionary tattoo techniques coupled with irezumi, the traditional Japanese style, birthed the experimental and now wildly popular neo-trad style.
This style is very popular for two basic reasons. First, the bold designs help the image age well. The thick outlines are less likely to fade over time. Second, it can be readily adapted to suit any aesthetic. It lends itself to being cute like a cartoon, but can also be easily modified into anime or even transformed into something dark and frightening.