Two sets $S$ and $T$ define the same germ at a point $\xi$ in a topological space $M$ if there is a neighbourhood $U$ of $\xi$ such that $S \cap U = T \cap U$.
Two functions $f,g : M \rightarrow \Bbb C$ define the same germ at $\xi$ if there is a neighbourhood $U$ of $\xi$ such that $f \vert_U = g \vert_U$.
Given a function germ $f_\xi$ and a set germ $S_\xi$, what is the meaning of $f_\xi \vert_{S_\xi}$?