Pixel Art
Pixel Art is normally seen in 2D games, comprised of 2D sprites to create a character or object. An example of a game that consists of pixels would be super Mario, back when it was 2D.

As you can see in this GIF the two versions of 2D Mario both contain pixels, as you can see by the square shapes on the image. Pixels aren't just squares, however it is one of the most common ways of identifying a pixel.

As you can see Pixels do restrict a game to being 2D as they are flat and do not allow for 3D graphics, also looking unrealistic it is not so ideal for a game that is aiming to be photo realistic.
On the left of this GIF you can see the very first version of Mario, which is restricted to few colours that do not look detailed at all, however the right version is a remake which has added colours which allow to define a character much more, as you can notice in the female character who looks very basic in the left and much more detailed in the right.

Concept Art

Concept Art refers to a character, weapon or the general environment in which a game takes place.

Digital Graphics

Raster images: These are in the form of BMP, GIF, TIFF, JPEG.
http://www.cambridgeincolour.com/tutorials/imagetypes.htm
JPEG - JPEG is a form of lossy compression, and is a file type that is used primarily for images with colour. With a JPEG the file size is normally smaller at the price of some image quality loss.

TIFF - TIFF files are larger than JPEG files, however they do not lose any quality as the files are not compressed like JPEG files, and TIFF files normally have a much better quality than other file types.

GIF - A GIF is usually an animated moving image, as you can see in this image below. GIF's do support static images as well, and are a form of lossless compression as they do not lose any image quality.


Vector Images
Vector images uses lines, curves or polygons in their images. This type of image is saved primarily in PSD, WMF, FIA, AI.
PSD - A PSD file is a layered image file format that consists of layers. Normally this file type is from a Photoshop file, so that the layers can individually be edited even if the file has been saved. http://whatis.techtarget.com/fileformat/PSD-Adobe-Photoshop-default

WMF - Stands for windows metafile, this is a file extension for files saved in windows. Orginally this file type was made for windows 1990, however it has since been adapted to support current file types.