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Probability density is the probability that an electron can be found at a certain location around the nucleus. S orbitals are spherical and symmetric, so there is an equal chance of an electron being at any point in the s orbital. P orbitals are lobes with a node in the center, telling us that at the ends of the lobes there is a high probability of finding an electron (high probability density) and this probability decreases as we get closer to the node until it is 0 at the node. It then increases on the other side as we go away from the node again. Psi is the wave function which specifies an orbital. Waves oscillate between positive and negative maximum and minimum values. Probability density must always have a positive value, (negative probability doesn't make sense) and squaring the wave function makes all the values positive. This is as far as you need to know for why the probability density is given by Psi^2 for this class.
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