What is the purpose of ../ in \input and \include?

Let us say you have the following structure:

LaTeXFiles (directory)
  foo.tex
  bar.tex
  test (directory)
    mwe.tex

Let us say you have the following line in file mwe.tex:

\include{../foo}

Then the file foo.tex in directory LaTeXFiles is included. So ../ means: go one directory back.

It simply used the path command available in windows with cd .. or cd test or cd LaTeXFiles/test or simular in unix/linux. Same with line

\input{../bar.tex}

It means the file bar.tex in directory LaTeXFiles is used in file mwe.tex.

../foo means that the file foo is located in the parent of the current working directory (one directory above it).

https://stackoverflow.com/a/23242061