Relationship between very ample divisors and hyperplane sections
Look at Chapter II Theorem 7.1, $\phi:X \longrightarrow P^n$ a very ample line bundle $\phi^*(O(1))$ is the pull back of O(1) bundle on $P^n$. But $O(1)$ is a hyperplance $H$, so in the image of $\phi$, the very ample divisor is the intersection of $X\cap H$