As part of trying to pinpoint what exactly an art style is, I think it would be best if I tried to properly define what the two main styles of visuals used in gaming are; 2D and 3D. Whilst what they are is immediately obvious, it would still be best if I quickly covered what each entails and some of the variations and best uses they have in the modern industry.
2D art styles were initially the only real option due to hardware limitations (Some earlier machines had the ability to display basic vectors but these were not truly widespread until around the fifth generation of consoles). However, as technology advanced, 3D became an option and 2D moved more into a choice rather than a restriction.
2D art styles work well for allowing hand drawn/designed assets to be used as close to their concept iteration as possible. This can work well for more visually expressive games with complex animations. Generally, 2D art styles are chosen because they fit the game genre or design. An example of this would be the fighting game or platforming genres. These genres are typically restricted to 2D movement and interaction and as such work well with 2D graphical assets that do not have to deal with depth or be rendered in a way that the camera angle is unknown. (NOTE – Both of these genres can also work well with 3D art styles as well)
As I stated in a previous entry, Pixels are also a staple of 2D art styles. When used appropriately, they can be incredibly appealing and they have fantastic range (Although most Art styles can be adapted to fit any theme if properly adjusted).
Many games mechanically chose 2D due to genre and fitting mechanics, but still use 3D art styles (Mighty number 9, TRINE ECT). Likewise some game that involve 3D movement and mechanics use 2D Art styles (South park : Stick of truth, Paper Mario).