an expectation value
If you prepare a huge number of identical quantum systems and measure the same observable on each, the results scatter, but their average settles onto a definite number. That number is the expectation value. It is the quantum theory's prediction for the mean of a measurement, and it is the bridge from the probabilistic formalism to the steady numbers experiments report.
For a normalized state |psi> and an observable A, the expectation value is the sandwich <A> = <psi|A|psi>, which in the position representation is the integral of psi*(x) A psi(x) dx. Written in terms of outcomes it is the Born-weighted sum <A> = sum_n a_n |c_n|^2, each eigenvalue a_n weighted by its probability |c_n|^2. The spread about this mean is the variance (Delta A)^2 = <A^2> - <A>^2, whose square root, the standard deviation, is the uncertainty that appears in the uncertainty principle.
Two honest points. First, the expectation value is a statistical average over an ensemble of identically prepared systems, not the result of any single measurement, and it need not even be an attainable value — the average position in a symmetric double well can sit exactly at the barrier where the particle is never found. Second, it requires many fresh copies each measured once, because a measurement collapses the state; repeating measurements on one system does not sample <A> in the same way.
For the ground state of a symmetric harmonic oscillator <x> = 0 by symmetry, yet <x^2> is nonzero; the difference gives a nonzero position uncertainty Delta x = sqrt(<x^2>) even though the average position is dead center.
A zero mean with nonzero spread: the expectation value is an average, not a typical single outcome.
<A> is an ensemble average over many identically prepared copies, not something you read off one measurement, and it may be a value the observable can never actually take.