I came across the following sentences which I cannot understand:
"In general, let $E$ be a vector bundle on a curve $C$, consider a point $p \in C$, and let $\xi \subseteq E_p$ denote a 1-dimensional subspace. Denote $E(\xi)$ to be the sheaf of sections of $E$ with at most a simple pole at $p$ in direction $\xi$."
Should I read "sections" as "sections of the vector bundle $E$ over the open $C \setminus {p}$"?
And what does "in direction $\xi$" mean?