From the kernel  (Documented)

Supply nothing at all

TeXSave["filename.tex"] converts the current notebook selection into .tex file with the supplied filename.

Supply an external, unopened notebook

TeXSave["filename.tex", "notebookfile.nb"] converts a notebook named  notebookfile.nb into a .tex file with the supplied filename.

Supply a NotebookObject

TeXSave["filename.tex", notebookobject] converts the specified NotebookObject into a .tex file with the supplied filename.