While digital refers to something that can be manipulated by the fingers (called "digits"), it also is a type of electronic signal that uses a binary code (a system using numbers, or "digits") to transmit information.
The Latin digitus means "finger or toe," so it makes sense that by adding the suffix -al, which means "being like," we get the adjective digital, "fingerlike." The idea of the word referring to numerals began around 1938, soon becoming vital in computers. It's easy to imagine the connection between fingers and numbers, as the first mathematical "calculators" were probably fingers and toes. Digital recording appeared in 1960 to challenge analog, soon becoming the broadcasting standard for clearer signals.