For external storage you can only write in the folder "NVIDIA_SHIELD", all other locations are read only. If you're using the external storage to manage different media files for example then you can create subfolders within the "NVIDIA_SHIELD" root folder.
SHIELD supports external storage that is formatted as FAT32, exFAT, NTFS, and HFS+. If your storage has been formatted differently, you can format it by insterting into your SHIELD's USB port and selecting Settings-> Storage & reset -> [Storage device] -> Erase & format as device storage