I understand the Taylor series and I understand what a germ is.
"Any vector $g = (z_0, α_0, α_1, ...)$ is a germ if it represents a power series of an analytic function around $z_0$"
And a sheaf is a set of germs.
But then I read
"Sheaves of analytic functions were once called multi-valued functions"
I am not sure how to make sense of this. Do they just mean that there are multiple vectors with the same $z_0$ but having different values for $α_0, α_1,...$?