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As far as I understand, electron density is the probability of finding an electron in a given spot. For example, the 1s orbital has uniform electron density, so there's an equal probability of finding the electron anywhere in the orbital.
Electron density represents the probability of an electron being present in a given space around the atom's nucleus, and is responsible for the shapes of the orbitals (which are mathematical functions that represent this probability).
It helps to understand how the wave functions (psi) in Schrodinger's equation are a mathematical representation of where electrons may be found. When we square psi to find the probability density, we are essentially able to understand which regions there is a greater probability of finding an electron. This is an important concept because it basically invalidates the "orbit" model. In nodal planes the probability hits zero, meaning that the probability of finding an electron is null.
In regard to Leda's answer, the first part is absolutely correct; however, electron density in an orbital is not uniform, it varies. The "shape" of the orbital is a visual representation of the wavefunction(psi) while electron probability density is psi^2. It is easy to mix them up! For an s-orbital, in general there is a greater probability of finding the electron closer to the nucleus. Figures 1D.4 and 1D.6 in the 7th edition (not sure which figures in the 6th edition correspond) are good visuals of this.
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