24 bit color is referred to as true color or full color because 16.7 million colors is enough to provide even the most subtle shading. 8 bit is typically recognized as a minimum requirement to provide reasonably natural looking color reproduction of complex images. 8 bits are often used to create a color index that refers to true colors. The number of colors a computer can show simultaneously is determined largely by the amount of memory available to the video display. For example, a PC may be able to provide 16 bit color at a resolution of 640x480, but only provide 8 bit color at 1024x768 resolution.
More powerful computers allow for more colors at higher resolutions.
Keep in mind that where hardware is concerned, the key principle is the number of colors that can be displayed simultaneously. However they may only be able to show as few as 256 at a time thereby limiting their ability to accurately reproduce images that require subtle shading. It's important to distinguish between the color content of an image and how it is displayed on different computers. A picture scanned at 24 bit color will look great on a computer that can display in 24 bit, but the same image will look pretty lousy on a system that's limited to only 256 colors. In other situations an 8 bit image can be displayed in very different ways by a single computer.