Why are cell phones called cell phones?

Mobile telephones use numerous low power base stations to communicate. As a phone moves, it can transfer its connection from one base station to another so that calls are not dropped while travelling. The base stations are called cells and together form a cellular network.
It is the base station technology that lent its name to the portable telephone in North America. Many other English speaking countries have different names for them with the term "mobile" being used in the UK for example.