The command might better have been as follows.
find ~/Downloads -iname "*.pdf" -exec mv '{}' ~/Documents \;
Note the semi-colon after the backslash. Or, also better as follows.
find ~/Downloads -iname "*.pdf" -exec mv '{}' ~/Documents +
Note the plus used instead.
Or even as follows.
find ~/Downloads -iname *.pdf -exec mv {} ~/Documents +
The single quotes around {} are used to tell the shell not to interpret the characters within the quotes as any kind of shell punctuation. They are normally not needed, but using the single quotes is not a bad habit to have. As far as I know, it's only fish that expands {} to something else. The {} characters themselves basically represent the list of found files.
The double quotes around the iname parameter are also not needed, but also not a bad habit to use them.
The command in the question uses the continuation character, so pressing Enter after it should only have provided another line on which you could continue to type. So, what else was typed after that command, or did you just forget to type the semi-colon in the question? If the command was typed as a regular user, then the PDF files may still be in your home directory somewhere.
It would have been most useful to open Terminal and type man find. Then see the section, Examples, for usage notes that would have covered this scenario.
To find all PDF files on your system:
cd && find / -iname "*.pdf" 1>found.txt
This will create a list, found.txt, of all PDF files that the regular user account has permission to list. I don't know if there is enough information to answer where the missing files have gone.
*. pdf2) Why does the command end in a line continuation (``)? You should probably include the next lines until the end of the command.\but I didn't escape it properly and it broke the code formatting.