NotebookSave[notebook] saves the current version of a notebook in a file.
NotebookSave[notebook, "file"] saves the notebook in the specified file.
NotebookSave[notebook, stream] sends the expression corresponding to the current version of the notebook to the specified stream.
notebook must be a NotebookObject.
NotebookSave[notebook] saves the notebook in a file whose name is given by the notebook object notebook.
NotebookSave writes out the Mathematica expression corresponding to the notebook, together with Mathematica comments which make it easier for the front end to read the notebook in again.
See The Mathematica Book: Section 2.10.3.
See also: NotebookAutoSave, NotebookPrint.