Open a terminal and execute this command:
mv -v ~/Downloads/* ~/Videos/
It will move all the files and folders from Downloads folder to Videos folder.
To move all files, but not folders:
If you are interested in moving all files (but not folders) from Downloads folder to Videos folder, use this command
find ~/Downloads/ -type f -print0 | xargs -0 mv -t ~/Videos
To move only files from the Download folders, but not from sub-folders:
If you want to move all files from the Downloads folder, but not any files within folders in the Download folder, use this command:
find ~/Downloads/ -maxdepth 1 -type f -print0 | xargs -0 mv -t ~/Videos
-maxdepth option specifies how deep find should try,
1 means, only the directory specified in the find command. You can try using
3 also to test.
See the Ubuntu find manpage for a detailed explanation