Wikipedia posits, in rather complicated language:
Telephone number mapping is the process of unifying the telephone number system of the public switched telephone network with the Internet addressing and identification name spaces. Telephone numbers are systematically organized in the E.164 standard, while the Internet uses the Domain Name System for linking domain names to IP addresses and other resource information. Telephone number mapping systems provide facilities to determine applicable Internet communications servers responsible for servicing a given telephone number by simple lookups in the Domain Name System.But that's not very helpful.
For most people, a phone number is tied to a phone. For some people, a phone number is tied to a house, or a business. More and more, though, we see phone numbers as being tied to a person. This is bound to happen, as our phones become seen as more and more an extension of ourselves.
While this tendency to associate phone numbers with people leads us towards powerful new communicative methods, it comes with dangerous risks. Anyone who has had to change to a new number can attest to the difficulty of doing so. Everyone you talk to has to be updated, and god forbid you forget someone, the consequences could be dire. This danger stems from the distinction between how we think about our phone numbers, and how the technology handles it.
I said earlier that phone number are often seen to be tied to people. The technology dictates that despite the way we think about our phone numbers, they must be tied to your phone. This is also why transferring your number to a new carrier is such a hassle.
There are several emerging services available to bridge this gap. They are all effectively call forwarding services, with a few extra features specific to recent technologies. I run my business on Google Voice, which allows my business number to be tied to me, whether I'm in my office, at home, or on the road. It's been very useful, and allowed me access to some neat tricks with my Android and iOS devices, which I'll get into another time.
While GV is what works for me, there are other call forwarding services out there. Phonebooth, Line2, and RingCentral all offer similar services, though generally with some variance to features or costs. I recommend taking a look at the various telephony services, and seeing if any of them could fit into your life.
Tying your phone number to you, instead of to your phone allows much more freedom from your phone carrier. Perhaps, with the right combination of apps and luck, a cell phone carrier could be made unnecessary.