The definition is on page 341, at the bottom. Basically, if $\pi'':X''\to X$, $\pi':X'\to X$ and $\phi:X''\to X'$ are birational morphisms of nonsingular projective surfaces such that $\pi'\phi=\pi''$ and $\phi$ is isomorphic (over $X'$) to the blow-up of a point $x'\in X'$, then by definition $x''\succ_1x'$ if $x''\in\phi^{-1}(x')$.