A Back in Time Save (BiTSave) is a glitch using BiT that allows you to teleport from any location to a statue you can access during Back in Time.
To perform a BiTSave:
The game will load your file at the statue you saved at in BiT, and BiT will end.
In fact, you do not necessarely need to have the file you want BiTSaved selected when saving. You need it to be the last file you selected before saving. But beware, if you save after opening the splash screen into file select you are not performing a BiTSave, but a File Dupe. When BiTSaving you should always manually select the file. The reason opening the Splash Screen doesn't work like expected is explained here.
A BiTSave changes your spawn locations. Your save location is set to BiT Skyloft, while your respawn location remains at the statue you saved at before BiTSaving. This makes it possible to undo an unintentional BiTSave. If you kill Link without saving or entering a new Area, you will respawn where you saved before you BiTSaved.
Also, if you quit and reload your file, you will end up in BiT Skyloft, but your respawn location will still be where you saved before the BiTSave. So dying and continuing will respawn you in that location.
When you BiTSave a file (for exemple to Skyloft but also in Faron for Faron BiT), the scene flag array isn't immediately updated for the new area. For exemple, if your file is saved in Eldin Volcano and you BiTSave it to Skyloft, then, while that file will state that it is now saved on Skyloft on the file selection screen, it will still have the flags from the area prior to the BiTSave (in this case, Eldin Volcano). To update the flags to be the flags from the new area, you will need to load your file and save at the statue properly again.
What this means is that it is not possible to combine a BiTSave with a Reverse BiTMagic trick, as the flag set during Back in Time will be set for the area prior to the BiTSave, but after starting the file the game will instantly load the flags from the new area, and the flag that was RBMed will be lost due to not have been committed properly.