Photoshop CS supports both 8 bit Mode and 16 bit Mode, which represents the number of bits used to store color information for each of the 3 RGB color channels.  With 8 bits, you can store 256 different values for each color channel, while 16 bits can store 256x256 = 65,536 different values for each of the 3 color channels.  In 8 bit Mode, you can represent 256x256x256 = 16.7 million different colors.  In 16 bit Mode, you can represent 65,536 cubed = 279 TRILLION different colors.  Although the 16 million colors may seem like a shipload of colors, it is not always enough.  The following 3 figures illustrate an example where the 16 million colors may not be enough in 8 bit Mode.  The original histogram is shown in Fig. 1 and a Levels adjustment is made to stretch out the range of intensities.  Fig. 2 shows the resulting histogram in 8 bit mode, while Fig. 3 shows the resulting histogram in 16 bit mode.  In 8 bit Mode, there are some gaps in the histogram in Fig. 2, while those gaps are not in Fig. 3.  This is not a real big deal in itself, but such gaps could be compounded by additional adjustments.  In some severe cases, "banding" can occur where you see color ridges.  To change from one Mode to the other, the menu path is Image > Mode > 16 Bits/Channel (or 8 Bits/Channel).
 
 

Fig. 1 Original histogram changed with Levels
Fig. 2 Resulting Histogram in 8 bit Mode
Fig. 3 Resulting Histogram in 16 bit Mode

If you are making substantial editing changes, then the higher number of colors is valuable.  For modest changes, additional bit depth does not make any noticeable difference.  There are some down sides using 16 bit Mode.  The file will be approximately twice as large and it will take about twice as long to perform some operations.  In addition, some filters and adjustments can not be applied in 16 bit Mode.  I use 16 bit Mode for all of my adjustments.  I also use the 16 bit Mode to resize my image up for making large prints at 300 pixels per inch.  However, after resizing up, I then convert back to 8 bit Mode and then save it before printing the 8 bit version.  By keeping it at 16 bit Mode during the resizing up, I maintain maximum accuracy.  Since my printer and my eyes gain nothing beyond the 8 bit Mode, I convert it to 8 bit Mode at the end.

For those who don't know 3 dimensional calculus, the following is one way of visualizing 3 dimensional RGB color space in 8 bit and 16 bit mode.  Fig. 4 (below) shows the 3D RGB color space as a cube full of colors.  Suppose you have a large room that is 256 inches (21 ft, 4 in.) in length, width and height.  Imagine that you fill up the entire room with 1 inch cubes (each of a different color) so that you would have 256x256x256 cubes, or 16 million cubes.  This is what you have in 8 bit Mode.  In 16 bit Mode, each cube would be 1/256 th of an inch on each side, which would be about the size of a grain of sand.  Then fill up the room with these tiny cubes and you see that there are many more colors, about 279 trillion of them.  Even though 16 million colors is huge, your image may only use a small number of these colors.  For example, if a room is "full of furniture," the furniture occupies only a small percentage of the volume of the room.  When you stretch out the histogram with a Levels adjustment from Fig. 1 to Fig. 2 above, your original image occupied cubes in about a half of the room and only those cubes are modified.  The net result is similar to filling up the room with 2 inch cubes, which results in 128x128x128 = 2 million cubes, which is only 1/8th of the 16 million cubes.
 
 

Fig. 4  RGB Color space from Color Vision