Misrepresentative box art refers to artwork on a game's packaging that in no way represents the look, theme, or general feel of the actual game. This misrepresentation can have the unintentional effect of making a good game look of poor quality, or it can have the opposite, intentional effect and make shoddy games look like quality products. In some cases, the box art has actually become more well-known than the actual game itself.
Quite possibly the most well-known example of misrepresentational box art is that for the North American release of the original Mega Man on the NES. Bearing absolutely no resemblance to the game's cute, Japanese aesthetic, the game's box art depicts Mega Man as a man in a blue and gold suit and helmet, wielding a pistol. The North American box art for Mega Man 2 was similar, in that it featured an adult human Mega Man in a blue suit with a helmet and visor wielding a laser pistol. Box art in later games eventually began to depict Mega Man as he was actually designed. As a part of marketing the downloadable title Mega Man 9, which was designed to intentionally resemble the old NES games, Capcom created a promotional "box art" image that drew heavily upon the absurd nature of the early box art designs as a nod to long-time fans of the series. They took the same route with the rapidly-produced sequel, Mega Man 10.
Another classic example comes from the SNES game Phalanx, a space shooter. Most people probably wouldn't realize this at first glance at the box, however, as the cover art is dominated by the image of a bearded old man with a banjo. The only hint of the game's actual nature depicted on the front of the box is a spaceship in the upper-right corner.