What is a Profile Mismatch and why does it always show up?

Question

b Question
Every time I open a file I get a prompt which reads: Embedded Profile Mismatch.
Embedded: Camera RGB Profile
Working: Adobe RGB (1998)
I always choose the default, which is the "embedded profile (instead of working space).
I have no idea what any of this means. I know that it started doing this after I chose something recommended in a Photoshop book.
Can someone please show me how to get rid of this prompt and point me in the direction of information that will help me choose the best profile?
b Answer supplied by Richard Rose
First the good news - your work flow is Color Managed.
Now the bad news - You have no idea what that means, nor how you are achieving that desirable situation.
You really need to start at the beginning and learn what color management is all about. For some reason lots of people get very confused and mislead trying to wrap their brains around the subject. It's really quite simple.
There are many named "color spaces" in which to work in Photoshop. you have chosen Adobe RGB (1998). You chose that color space in Photoshop CS under "Color Settings."
That's a good "general purpose" color space to use. It's very useful for workers preparing images intended for color reproduction in print (on a printing press). But it'll do for almost any use you have for your images. If your images are destined mostly for the Web, working in sRGB might be good. (I recommend just staying in Adobe RGB 1998)
The "short answer" as to why Photoshop needs to work in some particular "color space" is that the program must "translate" colors from their source (a digital camera, a scanner, a a graphics program) into a destination (display on a computer monitor screen, a particular printer, output for printing press reproduction, etc).
There are many compromises that take place in that translation process, and the requirements for all the possible conditions that must be satisfied (hue, saturation, how light or dark the image appears) cannot always be met. Something has to give somewhere.
Named color spaces (Adobe RGB, sRGB, Color Match RGB, Ekta Space, etc) make a number of assumptions and decisions about how color translations (conversions) should be carried out before Photoshop ever gets its hands on the image, and makes it much easier for Photoshop to carry out the conversions and maintain accuracy in converting (for instance) from a digital camera's idea of an image to the needs of your computer monitor (so you can see an accurate resemblance of the image) to the needs of a printing press, so that the image looks correct in a magazine.
The conversion process is carried out with the aid of "profiles." A profile is a set of data that is embedded in an image file that describes to any program that wants to read it, what the image data means in terms of color.
Without the profile, your digital camera's RGB file simply contains arbitrary RGB values. Yes, a particular pixel with high R values will be reddish, and another pixel with high B values will be blue, but the actual red or blue of those pixels as they relate to the original scene is unknown. The camera profile embedded in your file lets Photoshop know, to a high level of accuracy, just what hue of red, and just how much saturation is present, and how light or dark the red was in the scene. The profile's coding of this information is based on a color measurement system called CIE which uses several different mathematical models to carry out some VERY complicated computations. There are CIE Lab models, CIE XYZ, and others. These models are as close to an "absolute" color reference system as we have.
Thank God you are using camera files that actually have profiles! When you open such a file, Photoshop is "warning" you that the image information is in a color space other than the default Adobe RGB space. You told Photoshop to warn you about such "mismatch" when you set Color Management Policies in the Color Settings section.
Photoshop is telling you that "something" needs to be done. It can honor the camera's color space, from it's own frame of reference (Adobe RGB 1998) and work on the image, accurately handling the color information for screen display and eventual output. That's what you tell it to do when you "accept" the embedded profile. That's not bad, everything will work correctly, because Photoshop will have made internal conversions that remain active as long as the file is open, but there is something you have to keep in mind - when you save the file, Photoshop will save the original camera profile with it. Then if you open the file again, the same "warning" will occur.
That camera profile is as valid and useful as any other profile, but because it is not a commonly recognized color space may cause a problem in some other workflow. (Notice I said MAY. ICC color profiles SHOULD be ok in any program)
It is probably better to choose "Convert to working profile" on opening the file. From that point on, nothing will appear different to you, because nothing has really changed. Photoshop will handle the file as it did before, internally converting the color information as necessary with regard to its working space. But when you save the file, the Adobe RGB 1998 profile will be embedded in it. If you re-open it, you will get no mismatch warning, and the file will be recognized by most other image handling programs as having a "standard" color space.

Answer 1

Thanks! I still don't understand the concept of "saving power" in this context. Does that relate to a laptop running on battery, and some popups consume more battery power? Or does this refer to CPU capacity?  I have never had any issue that I know of in these areas. I would understand the warning if it cautioned me about insufficient bandwidth, but that doesn't seem to apply here. In any case, am glad to find that this is a feature and not a bug.
Stan