What is Wavefunction?

The state of an electron is described by a wavefunction $\psi(x, y, z)$; $|\psi|^2$ is its probability density: the probability of finding the electron in a small volume $dV$ around a point is $|\psi|^2\,dV$, and $\int|\psi|^2\,dV = 1$ over all space (the function is normalised). An atomic orbital is the wavefunction of one electron in an atom.