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The probability of electron density is simply the probability of finding an electron in a certain location (i.e. a particular orbital). It is described as a probability because we can never be certain of an electrons position at any given time. What you are referring to is the probability of an electron being in a particular orbital.
To my understanding, because of the Heisenberg Uncertainty Principle we can never exactly guess where subatomic particles, like electrons, can be located at a given time. Because of this, we use the wave function to give the probability density of an electron at a given point, which basically means what is the probability that you are going to find an electron at that point and time. Then, having a higher density means that there is a higher chance of finding an electron at that point.
It's the probability of an electron being present at a specific location, aka in a specific orbital. The reason this is uncertain and not exact is because the exact position and momentum of an electron cannot be determined at the same time. Electrons are just too small and fast, man.
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