Write mode toggles whether or not information may be written to a device. For example, a floppy diskette has a write mode tab can be slid up or down. When in write mode, the diskette can have information written to it, but in write protected mode, none of the disk's contents can be modified.
With software and software settings, write mode is a permission instead of a physical tab. For example, if a file is set to read-only, the information can only be read, but not changed.