A classical bit has a definite value: 0 or 1. A qubit is different. Before you measure it, its state is described by two amplitudes -- one for $|0⟩$ and one for $|1⟩$. These amplitudes are not probabilities. They are the deeper quantities that produce probabilities when you square their sizes. They also carry phase, which is why a qubit is richer than a random coin flip.

Think of a recipe versus a meal. The quantum state is the recipe -- it tells you what outcomes are possible and how they relate. The measurement result (0 or 1) is the meal you actually serve. The recipe contains more information than any single meal.

The symbols $\alpha$ and $\beta$ are complex amplitudes. Their squared magnitudes give the measurement probabilities in the standard basis: P(0) = |$\alpha$|² and P(1) = |$\beta$|². Because $\alpha$ and $\beta$ are complex numbers, they also encode phase information. Two states can have the same measurement probabilities but different phases, which means they will behave differently in future operations.