The answer from @ISanych is correct but incomplete. I spent almost an entire day trying to achieve what I know now is not possible using the Docker COPY command. I read many issues similar - but not quite the same - as mine on the internet. I hope the explanation below will prevent another user from making the same mistake.

COPY will copy the contents of each arg dir into the destination dir. Not the arg dir itself, but the contents. https://github.com/moby/moby/issues/15858#issuecomment-136552399

I don't know this user but this is the most authoritative and clear description of the difference in behavior that I have found (the emphasis is mine)

The OP has the following structure and would like to recursively copy the contents of the files directory into a similarly named files directory already existing on the image file-system.

files/
   folder1/
     file1
     file2
   folder2/
     file1
     file2

The OP used the following command

COPY files/* /files/

and was surprised to learn that rather than copying the two folders folder1 and folder2 and their contents into the files directory the command actually copied the contents of folder1 and of folder2 into the files directory. As explained by the moby developer above in the full response in the Github issue, the shell glob (*) will expand to pass in folder1 and folder2 to the COPY command which will then copy the contents of each of folder1 and folder2 into the destination folder.

If you use the approach suggested by @ISanych - COPY files/ /files/ - then the contents of the files directory - that is the directories named folder1 and folder2 - will be copied into the destination /files/ directory as indicated.

Importantly, there does not seem to be any way to avoid this behavior of the COPY command. This behavior is highlighted (as it was for me) in the situation where there are multiple source file structures similar to that described by the OP and the user wishes to copy several top-level directories recursively into the root directory on the target - in one go:

files1/
   folder1/
      file1
      file2
   folder2/
      file1
      file2
files2/
   folder1/
      file1
      file2
   folder2/
      file1
      file2

Using the docker COPY command as you would the *nix cp command will yield unexpected results. That is, writing the command COPY files1 files2 . will not behave in the same way as a similar GNU cp command. Instead the COPY command shown will yield the result in which you have the contents of files1/folder1 and files2/folder1 merged into a single folder1 on the destination and you are left with something like this and wondering what happened to the second (or first) directory?

   folder1/
      file1
      file2
   folder2/
      file1
      file2

If you wish to recursively copy the directories and their contents to a destination directory from the build context, the work-around is to create the destination directories first with the desired name and then issue a COPY for each of the top-level directories. E.g. for the files1 directory:

RUN mkdir ./files1
COPY files1 ./files1
RUN mkdir ./files2
COPY files2 ./files2