A classical computer stores information in form of bits. A single bit is can be in state 0 or state 1. A string of 8 bits is called a byte. For example, a byte encoding a number 15 is 00001111 (“add 1 + 2 + 4 + 8, skip 16, 32, 64, 128”). A CPU is a device shl, shr, add, sub, mul, div, mod, and, or, xor.
A quantum computer stores information in form of probability amplitudes, which are complex numbers. A single qubit $\lvert\psi\rangle = a\lvert 0\rangle + b\lvert 1\rangle$ has two complex numbers.