I read this paragraph from Complex Geometry by Huybrechts:
...The pull-back of a divisor $D$ under a morphism $f:X\rightarrow Y$ is not always well-defined, one has to assume that the image of $f$ is not contained in the support of $D$. Thus, one usually considers only dominant morphisms...
So why would the pull-back be not well-defined if the image of $f$ is contained in the support of $D$? And why does dominant morphisms solve this issue?
Suppose you are working with weil divisors on a regular variety. Then, effective divisor correspond to codimension 1 subvarieties. In this case, if the image of $f$ is contained in the support of $D$; then the pullack would be all of $X$, which is not a divisor.
Taking a dominant morphism solves the issue, because then the image of $f$ will be an open subset, and a codimension 1 subvariety of $Y$ cannot contain any open subset.