We have always heard that it's better working in 16bit mode in PhotoShop or other image editing apps but the demonstrations I've seen talk about theories and odd histograms.
Here goes a detailed procedure to see live by yourself how it can make a change when you do process the image.
What we will do is create a black to white gradient apply two exaggerated curve layers to that image and see the result in both modes, 8 and 16 bit. Before starting it's important that you have your monitor color resolution right, it must be configured at 24 or 32 bits color quality so it displays accurately the color gradations.
First let's create a new image with a width about half to 3/4 of your screen, here we will work with one 700 pixels wide.
Create a new document in 8 bit mode (menu File->New) 700 wide and a height about 350. Make sure it's in 8 bit mode.
Now we will fill that document with an horizontal uniform gradient from black to white.
<-- Choose colors Black & wide and the Gradient tool.
Hold down the shift key, click the left side of the empty image and drag the mouse to the right side. You should end with an uniform gradient, something like this:
OK, now let's simulate some heavy operations on this "image".
Create a new adjustment layer curves (menu Layer-> New Adjustment Layer->Curves.
Drag the top/rightmost point down to the value 32, so below the graph and
with that point selected you should see
Input:255 Output: 32
(No one would do this to any of his precious pictures but we are exaggerating things to see the effects clearly)
And now create a new curve layer like before but to balance the previous operation.
For this you will have to move the top/right point to the left so
Input: 32, Output: 255
Ideally the result image should be the exactly as the original with that smooth gradient but what you have is a series of bars clearly differentiated with abrupt transitions from one to the next (posterization)
What happened is that the values that represent all the original hues of gray got truncated at the first operation (curve).
In fact what we did with the first curve was to divide each value by 8 so some pixel value being for example 128 got to 16 but a value of 123 fell off to 15 (123 divided by 8 gives 15.375 but digitally this 0.375 subtlety got lost due to the need to truncate to an integer value -no decimals-)
With the second curve we did the inverse, multiply each value in the image by 8, the value 16 we got from 128 goes back to the original value 128, good for him, but our 15 (coming from 123) multiplied by 8 goes to 120! It makes quite a difference as it should have ben again 123 . Do the same reasoning for 122 and you will see that it also goes down to 15 and back to 120. This explains why something that what was a set of smooth continuous values goes to that jumpy result:
Now comes the fun. You have the base layer with the original smooth gradient and the two operations in layers that should neutralize each other but that spoil it.
Just change the image mode to 16 bit (Menu Image ->Mode ->16 Bits/Channel) (IMPORTANT do not flatten the image if you are prompted to do so!) ... and hops! all the lost subtleties are back! (if all is going well now you should see the image as it was originally, no posterization)
16 bits mode has much more values to represent the data and we can not perceive the lost hues due to these heavy operations. As the operations are in layers changing to 16 bit mode forced photoshop to transform the original data and apply on top the curves giving a good (smooth gradient) result.
When you do curves and other operations on your images something similar happens, obviously not to such heavy degrees but they are there and can easily degrade the image quality as the effect may be accumulative. While in 16bits everything is much more refined.
Now that you have this image with the adjustment layers, try converting it again to 8 bit mode. You see posterization again, OK. But revert back to 16 bit mode, FLATTEN the image and convert to 8 bit. Wops, now there's no posterization!. That's because the operations were done in the 16bit domain, flattening removed the operations and left a final image that when converted to 8 bit could keep the continuity in hues.
Conclusion: Whenever possible work in 16bit mode. If you have to use a 8 bit file (a jpeg file is) convert to 16bit when you load the image if you will retouch it. If you need to convert to 8 bit, first flatten your image and do the conversion to 8 bit the last.
Finally one example of a real world image with the same treatment in 8 and 16 bit modes:
© Juan Trujillo Tarradas.