In A. Andreotti On to Theorem of Torelli American Journal of Mathematics Vol. 80, No. 4, pp. 801-828, it is written:
Let $ f: X \longrightarrow P $ be a rational map of a projective irreducible variety of dimension $d$ on a projective space $P_d$.
Let $A$ be the set of points $y \in P$ such that $f^{-1}(y)$ consists of $n$ distinct points. The minimal algebraic variety containing the complement of $A$ (i. e. the closure of the complement of $A$) will be denoted by $D$.
The pure part of dimension $d -1$ of $D$ has an intrinsic meaning in terms of the extension $k(P)\subset k(X)$ and the chosen model $P$ of $k(P)$. It will be called the branch locus of the rational map $ f: X \longrightarrow P $.
My question is: what does "The pure part of dimension $d -1$ of $D$" mean?