If you are emailing with the professor for one of your courses and they sign their email with their initials $($e$.$g$.,$ if their name is Jane Smith but they sign their email $"$JS$")$ what does that mean?

That means that they still want you to address them with their proper title $($e$.$g$.,$ Professor Smith$),$ but they are writing quickly and$/$or want to seem casual.

That means that you should address them in future emails by their initials, e$.$g$.,"$JS$".$