In quite a few papers I've found the following definition of Hecke transform of a vector bundle.
Let $E$ be a vector bundle on a smooth projective curve $C$. Let $p \in C$. Then the Hecke transform is defined as the kernel of $E \to E_p/L$ where $L$ is a line in $E_p$.
$E_p$ is the firbe of $E$ at $p$ and as such is just a vector space. I'm not sure what the map is from $E \to E_p/L$.
Any insight is helpful. Also, why do we care about this kernel?