When the wavefunction, \(\psi\), is squared the result is a number that is directly proportional to the probability of finding and electron at specific coordinate in 3D space. The radial portion of the wavefunction really only tells us if there is high or low probability at various distances from the nucleus (possible radii for the electrons). Multiplying this probability by the area available at that distance will give us the Radial Distribution Function for the given electron. The concentric spherical shells have areas equal to the surface area of a sphere which is \(4\pi r^2\).
Although the calculus/math can be very complex, we can still view these plots and easily interpret the fact that there are distinct regions outside the nucleus where there is the best chance of finding an electron with a given set of quantum numbers. Below is a plot showing the first three s-orbitals for the hydrogen atom (1s, 2s, and 3s). The maxima for each plot shows the distance (\(r\)) from the nucleus for this region. Remember that in spherical coordinates, this maps to a spherical region in space. All \(s\)-orbitals are spherically symmetric.
What you need to notice: Note that the greatest probability for the 3 curves progresses to distances further away from the nucleus (nucleus is at zero). So you conclude that a \(3s\)-orbital is slightly larger than a \(2s\)-orbital which is slightly larger than a \(1s\)-orbital. And, even though we don't show more orbitals, you can conclude that the trend will continue for the \(4s\)-orbital all the way through to the \(7s\)-orbital.
Overall Probability of finding and Electron: We know that the electron must be somewhere in space around the nucleus. So the total sum of all probabilities at all distances must be 1.0 or 100%. The area under each curve will be equal to that overall probability. These means that every curve in a radial distribution plot should have an integrated area (think calculus integration here) equal to one.