What is the importance of binary numbers in the operation of a computer?

Because, a computer can only understand binary numbers(0s and 1s). Actually, they are represented internally as voltage levels, a positive voltage level to represent 1 and a 0V to represent 0, generally represented as ON and OFF. The voltage levels are dependent on the implementation so even a -5 can be interpretted by the computer as a 0 and +5 as 1,etc.