The color depth of a GIF image is 8 bits per pixel. Each pixel stores an 8-bit index, allowing it to refer to one of as many as 256 entries in the image's color palette.
GIF's palette does not contain arbitrary full-color values for every pixel. Instead, the palette entries are selected from the much larger 24-bit RGB color space, which can represent millions of possible colors. This distinction is why GIF files are commonly described as 8-bit images even though their palette colors are defined using three 8-bit color channels.
The 8-bit limit reflected the display hardware of the 1980s, when 256-color graphics systems were widespread. Dithering could imitate additional shades by placing nearby palette colors together, but it could not increase the true number of colors available in a frame. Animated GIFs can assign separate palettes to individual frames, though each frame still normally remains limited to 256 colors.