|Try looking at some information I found on the Adobe website:|
It says that PDFs can contain transparent objects. I imagine that if an author wanted to put the word "COPY" diagonally across a page in big grey letters, the author might use a transparent object. The object might be stored once in the PDF but have to be applied to dozens of pages. The process of applying the transparent object to many different pages and determining the final appearance of each page is "flattening".
I don't know much about this process in Adobe, but this usage roughly corresponds to the way the word is used in computing in general.