The binary system is a numbering system that uses only two digits: 0 and 1. It is the foundation of all digital computing and information storage because computers use electronic switches that can be in one of two states, represented as 0 or 1. In contrast to the decimal system (base 10) used by humans, where each digit represents a power of 10, in the binary system, each digit represents a power of 2. This system is crucial for representing and processing information in computers at the most fundamental level.