Intuition behind the degrees of freedom in ridge regression

Question

I'm reading through the ESL book and I'm on the part of ridge regression where the effective degrees of freedom are defined $$ df(\lambda) = tr(X(X'X + \lambda I)^{-1}X') = \sum_{j=1}^p{\frac{d_j^2}{d_j^2 + \lambda}} $$

I have no idea where this is coming from, what's the idea and intuition behind it.