You need to run a batch file, this can be either initiated at the PC end for which you need a pre-made tool, similar to one offered in http://www.dirsyncpro.org/ (No Affiliation nor have I tested this personally).
However if you dont want to use a tool, you could do it from the USB drive end, which means as soon as a specific USB is inserted, it will "look" for a folder in your hard drive and copy it onto itself (overwriting any previous version without asking)
xcopy /e /y c:\<yourfolder>\*.* .\dir_on_usb_drive
xcopy is actually deprecated now in favour of robocopy which is not the scope of this answer, but basically you need a recursive copy command that can copy the entire content (robocopy also offers resumption and retrying partially copied files which would help you)
Once you have the command ready you can add it to a batch file and create an autorun.inf file inside the USB (this is one structure - Warning Untested Script ahead)
action=Backup Your Files
You will now see this as an option in the autorun menu of windows when you insert the USB drive (with description as "Backup Your Files" which was provided in autorun file.