File Save lets you save your file either by its extension e.g. save a file.xcf as an XCF image. The XCF file format is GIMP's native file format and is the preferred format to save all your images in.
You can of course save as TIFF, JPEG, or one of the other available formats, but all the specific GIMP image information will be lost (i.e. the information about layers, channels, parasites, selections, etc).
When you save an image in a non-GIMP format (i.e. not as a XCF or XJT image) you could be asked to export it. By exporting it, you will be sure of getting all the visual image information saved in the non-native format (exporting will, for example, flatten an image to be saved as .jpg). Ignoring the suggestion to export runs the risk of losing valuable image information such as nonactive layers.
The Save dialog works like any other file dialog, but you also have two means of fast navigation. TAB completion, if you have a directory /gimp and the Save dialog is currently with in the /home/gimp directly. Then you only have to type /gi and hit TAB and the name will be completed (it works just like TAB completion in the bash or tsh shells in UNIX or if you have turned it on as TAB completion in the cms in NT). You also have a drop down directory menu which will enable you to quickly move up in the directory hierarchy.
You can also create directories and delete or rename files in the Save dialog. Sometimes it is necessary to step up and down once in the directory hierarchy before GIMP will be able to see the new directory.
Default Keyboard Shortcut: Ctrl-S