What is the use of selection like blue box in pdf apps? What could be the use of that selection like blue box(see the + sign and box from by it) which can be formed when we right click and drag in files like pdfs? on home screen this will be useful for multi selection of icons, so what is use of it in pdf? its is not selecting anything when we start dragging at some empty place.

If its not having any function then why is it present?
It is used for selecting content in the PDF. The selected content could then for example be copied to the clipboard.

Note that not all PDFs have content which can be copied in this way.