What does linearly equivalent mean in this context

Question

I'm trying to understand this proof of Fulton's algebraic curves book page 107:

I didn't understand what does linearly equivalent mean in this context and why this implies it suffices to show that $\text{div}(\omega)=E_{n-3}+\text{div}(f_y)$.

Thanks in advance

Answer 1

Two divisors are linearly equivalent if they differ by a principal divisor.