probability amplitude
A probability amplitude is the complex number quantum mechanics assigns to a possible event or outcome. Its magnitude squared gives the probability of that outcome, but the amplitude itself carries extra information the probability throws away: a phase, like the direction of a tiny arrow. The wavefunction ψ is precisely a continuous collection of such amplitudes, one for every position.
The reason amplitudes, rather than probabilities, are the fundamental quantities is interference. When an event can happen in several indistinguishable ways, you add the amplitudes for each way and only square the total. Because each amplitude is an arrow with a direction, two of them can point oppositely and cancel, producing a place where nothing lands even though each route alone would have delivered particles there. Ordinary probabilities, which only ever add, can never do this.
Amplitudes obey a clean rule of thumb: amplitudes for alternative paths add, while amplitudes for steps taken in sequence multiply. This simple grammar, with the final magnitude squared by the Born rule, reproduces the entire strange catalogue of quantum behaviour — the double slit, tunnelling, and the rest. The amplitude is the hidden, phase-bearing layer beneath every quantum probability.
Amplitudes are complex and add before squaring, which is exactly what lets quantum paths interfere.
An amplitude is not a probability and is not directly observable. Only its magnitude squared is measurable; the phase reveals itself only indirectly, through interference.