The friendly version
A classical bit is a switch: definitely 0 or definitely 1. A qubit is built from something tiny (an electron, a photon, an atom) and tiny things can hold a genuine blend of both possibilities at once. When you measure, the blend snaps and you get a plain 0 or 1, with probabilities set by the blend. The full spinning-coin story is in What Is Quantum?
Let op: analogie: the spinning coin is a teaching picture. Where it breaks down: a real coin has no phase. No hidden angle that makes later outcomes reinforce or cancel. Qubits do, and that phase is where all the computing power lives.
The state, precisely
A qubit is a two-level quantum system. Before measurement, its state is written as
|ψ⟩ = α|0⟩ + β|1⟩
The complex numbers α and β are probability amplitudes. Measured in the computational basis, the probability of 0 is |α|² and of 1 is |β|², summing to one. Represent |0⟩ as [1,0]ᵀ and |1⟩ as [0,1]ᵀ; a general pure state is [α,β]ᵀ with |α|²+|β|²=1. Global phase is unobservable; relative phase drives interference. Two states with identical immediate measurement probabilities can behave completely differently later. This is why a qubit is not merely a random classical bit with an unknown value.
The Bloch sphere
A pure single-qubit state can be written cos(θ/2)|0⟩ + eiφ sin(θ/2)|1⟩; the Bloch sphere is the geometric map of θ and φ. Mixed states require a density matrix and live inside the sphere. Measurement need not be in the computational (Z) basis. Rotating before measurement effectively measures in X or Y, and basis choice determines what information is revealed.
The picture above is a map of everything a single qubit can be. The north pole is 0, the south pole is 1, and every other point is some blend. It is a chart, not a photograph of a tiny spinning ball.
The correction that matters
A qubit is not literally "0 and 1 at the same time." It is a coherent quantum state with amplitudes for the two outcomes. Measurement returns one bit per run, which is why quantum algorithms run circuits repeatedly, collect samples, and infer answers from the distribution. Whole categories of hype dissolve once this sentence lands.
Going deeper
The full formalism (Hilbert spaces, density operators, POVMs and channels) is covered in the Academy's advanced course, Quantum Information Formalism, with the information-theoretic limits (no-cloning, teleportation, entropy measures) in the following module.