This analogy may help clarify some Color Management concepts. 

Disclaimer

Be careful with analogies. They are useful for clarifying a principle but it is always dangerous to dig into them in an effort to discover additional truths about a subject. This analogy is no different. 

Bringing Order out of Chaos

Color Management works a lot like an international banking system. Instead of wrestling with all the possible exchange rates (which would be N!/((N-2)!*2) where "N" is the total number of currencies and [!] indicates a factorial) involving each currency of each participating nation, the bank identifies one currency (or some other negotiable entity such as gold) as a standard and then manages exchange rates between each currency and this standard. When someone wants to exchange an amount in one local currency for the equivalent in another, his amount is first expressed in an equivalent of the standard at the prevailing exchange rate and then that amount (of the standard) is used to purchase the equivalent in the second local currency. In this way, only "N" exchange rates must be managed (one between each local currency and the standard). The penalty is that you must do two calculations instead of one but it's a small price to pay for the convenience of avoiding exchange rate chaos.

You could think of the monetary standard in this case as the Profile Connection Space (described in the Introduction) and the local currencies as individual device color spaces. The exchange rates are analogous to the calibration process.

So, when we want colors and tones representing an image living in one color space (let's say it's a monitor calibrated to Adobe RGB) to retain as much as possible of their appearance when moving them into another color space (a printer, perhaps) we first find where those colors are in the standard Profile Connection Space (PCS). We then reverse the process, using the subset of PCS colors thus selected to select equivalents in the target color space. The colors in the image will now be represented by different RGB triplets (not the same as either the source or PCS subset numbers) but, ideally, they will look the same.