If I say, $f|_{k}$, what does that mean?

Question

If I say, $f|_{k}$, what does that mean? Sorry to be short on words but I can not find it anywhere on google so maybe someone could explain it and what we typically use it for. I ran into the notation in a book and they do not explain what it is.

Answer 1

It means that if $f$ is defined on the set $X$, and $k \subseteq X$, then $f|_k$ is $f$ restricted to the set $k$.

Answer 2

It might also have the meaning that $f$ is a modular form, and $k\in\operatorname{SL}_2(\mathbb Z),$ and $f\mid_k$ is $f$ under the action of $k.$
Compared to the answer of @Johanna, this shows that, if the context is missing, the meaning of this symbol is not fixed at all.
Hope this helps.