If you walk past an electrical retailer with a row of TVs in the shop window, you'll notice that the skins tones and other colours look different on each set. The differences may be subtle, and no TV is necessarily any more "correct" than any other. But each TV will have a control that lets you tweak the colour until you match what you are seeing with what you expect to see i.e. colour management (color, if you don't speak standard English).
Gamut
A TV is but one type of device; now imagine a series of devices, each unique in the way it handles colour. What are the chances that an image will look the same as it passes from your camera, through your monitor, to your printer? Slim, if the range of colours available (the gamut) on each device differs widely and you're not using colour management.
Colour spaces
A colour space is a 3D representation of the gamut (colour range) for a particular device (see the graphic below). The aim of colour management is to match a particular tone in the colour space of one device to the same tone in the colour space of another device. For example, in the RGB colour model values are made up of three numbers corresponding to Red, Green, and Blue. So the specific tone of grey defined by 190,190,190 on one device might match up to a different numeric description on another device.
Device profiles
For colour matching to happen, each device must have a device profile made of its own gamut. This serves as a basis for translation: if colours captured/ produced by both devices "A" and "B" can be mapped to a known colour space "X", then colour data transferred from one to the other device has (approximately) "sameness". Approximate, because your monitor cannot physically reproduce the full colour range that your camera sensor captured, and your printer inks cannot physically reproduce exactly what you see on screen—but it should be near enough.
Working spaces and image profiles
Let's not, however, forget our image - which still has to get from one device to the next! When we "free" an image from the device used to capture it and open it in ACR and/or Photoshop for processing, we need some way of "tagging" that image with information about the colours it contains (which will very likely change during editing). If we don't do this we have broken the flow of information about colour running from capture, through processing, to output. Enter various arbitrary colour spaces that are not device-specific, with gamuts of varying size and names such as sRGB (small), Adobe RGB (larger), and ProPhoto (larger still). Collectively such device-independent colour spaces are called working spaces. When we assign one to an image, we create an image profile and in the process effectively make our image itself independent of the colour characteristics of any hardware device used to capture or output it. The relative size of the three spaces mentioned in the order listed above can be seen in the following graphs, taken from Apple's ColorSync Utility:

Importantly, just as we can translate between device profiles, we can also translate between image profiles (i.e. move from one working space to another). If you translate from a colour space with a small gamut to one with a larger one, your original colour range will be contained without clipping. The reverse is true, however, if you translate from a colour space with a large gamut to a smaller one, where some of your colour data are likely to be clipped. Clipping is illustrated in the histograms here.
ProPhoto is a preferred working space for digital photography, although is not without potential problems. Apparently the Adobe RGB (1998) colour space is popular; Kelby recommends it over ProPhoto saying that latter "lets you add colours your printer can't reproduce". However, the aim during raw conversion is to work with as much of what the sensor captured as possible: the histograms here sold me on ProPhoto for raw images. You can always convert to a smaller colour space later—but you can't subsequently add colour information that has been lost at the time of raw conversion.
Note: In-camera colour space settings restrict the colour range recorded to JPEG, but the camera sensor can capture a larger gamut (hence the value of shooting raw). ACR 3.1 used with Elements doesn't give you a choice of colour space, but Elements itself is limited to using sRBG or Adobe RGB. Note also that colour space isn't the same as colour mode; the latter refers to how Photoshop (by default) and your display represents colour (using three channels—red, green, and blue or "RGB"). An alternative colour mode (or model) is CMYK, used in professional print processes. Evening says that Adobe RGB is "particularly suited for RGB to CMYK conversions".
Colour management systems
The job of colour management software is to manage the translation of colour data between device profiles and image profiles, relative to a standard reference based on a measure of human colour perception (the colour space "X" referred to above). The system used inside Photoshop is called "ACE" for Adobe Color Engine (see Edit > Colour Settings > More Options). ColorSync is Apple's implementation of the ICC (International Color Consortium) colour management system. ICC profiles can be used by any colour management system that recognises them (so Photoshop "knows" about your ColorSync-managed display profile, for example). Although ready-made ICC profiles are available for many devices (not for my HP OfficeJet d135), it may be possible to customise your own. ICC profiles that combine printer + specific paper types exist too, but this is less relevant if you'll be using an online lab for prints like I do. I have an Apple Studio Display (which ColorSync automatically detects), so this is the profile that Photoshop automatically uses to display colour on my screen:

With the "factory" profile as a starting point, you can calibrate your display subjectively using the Display Calibrator Assistant to better reflect your unique hardware, local lighting conditions, current phase of the moon, etc. You are supposed to calibrate (professionals will spend $US300+ on an objective colourimeter), but it's hard to see the point when lighting conditions are highly dynamic (sunny, overcast, noon, dusk, desk lamp, ceiling light, etc.). That said, mine is set to Television/ PC gamma (2.2) and D65 as the white point ("warmth") so I can guestimate what Windoze users will see.
I have Photoshop CS2 set to North America Prepress 2 (Edit > Color Settings...) as this defaults your working space to Adobe RGB rather than sRGB. Kelby suggests setting the RBG colour management policy to "Convert to Working RGB", but this will slim down your ProPhoto working space (as set in ACR) to the smaller Adobe RGB one when you open the converted image in Photoshop proper. Leaving things set as they are shown in the following screen shot will preserve your ability to work with raw images in the massive ProPhoto working space, and at the same time lets you work with JPEGs and other non-raw files in the modest-sized Adobe RGB working space:

So, how does this all fit together?
It's time for a pretty diagram:










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