It's perfect way to keep at hand all important files if you don't have iBridge around. Local Storage uses iPhone’s internal memory to store files and you will be able to access them without plugging in iBridge.
How to transfer files to Local storage? In order to copy or move file to Local Storage you can use File Manager. (Select the file you want to move to Local storage, tap on 3 dots and select Move to...Local Storage and choose the destination fonder).