Depending on whether your data were standardized or centered, the loadings are the correlation or covariance, respectively, between your columns of data and the eigenvectors.

What do loadings mean practically?

The loadings are easiest to interpret when you chose to analyze standardized data. Each loading value corresponds to a single variable and a single component, both of which are just a set of values. The loading is the correlation between the values of the variable and the calculated values for the component. Because the loadings are correlations, they always have values between -1 and 1. For example, the loading of -0.852 between Radius and PC1 indicates that PC1 is strongly correlated with Radius, and that as Radius increases PC1 decreases.

If you chose to analyze centered (rather than standardized) data, then the loadings are not bounded by -1 and 1. In this case, you can still use the loadings to interpret the strength of the relationship between the variables and eigenvectors, but only relative to the other loadings.

How are loadings, eigenvectors, and eigenvalues related?

Like this: Loadings = Eigenvector * sqrt(Eigenvalue)