The classical computer (non-quantum), like the PC or laptop that sits in front of you, uses the language of computers called binary. Binary is a base 2 mathematical language because it only consists of two digits. These are 1s and 0s. This is the fundamental unit of information or building block called the bit. A bit, in classical computers, is either a 1 or 0. In quantum computing the fundamental unit of information is a qubit (quantum bit). Qubits form the basis of quantum computing.
Perfect, but what makes a qubit different from a classical bit. Let us look at the following example to demonstrate the radical contrast between the two. In a classical computer, let us say we have two bits. These two bits could consist of one of the following combinations: 00 or 01 or 10 or 11. In quantum computing, two qubits can also consist of one of those four abovementioned combinations which are called computational basic states. Now, here is the crux of quantum computing. While a classical pair of bits can store these numbers only one at a time, a pair of qubits can also exist in a superposition of these four basis states or between 0 and 1. What this means is that a pair of qubits can simultaneously consist of all four possible states or combinations (00, 01, 10, 11). Thus, qubits can contain an extremely vast amount of information (in fact, in theory, an infinite amount of information) and this results in quantum computers being exponentially more powerful than classical computers (non-quantum).
This unique property of a quibit (to be able to exist in a superposition of states) arises because of quantum computers following the laws of quantum mechanics, while a classical bit follows the understood laws of classical physics.