Premultiplication is a procedure that can be applied to a partially transparent image file. The result is an image that can be composited onto a background more quickly and efficiently.
The problem is that some software packages produce (or expect) image files that have been premultiplied, and some produce (or expect) image files that haven't been. And there is no good way for a computer to tell whether an image has been premultiplied or not. A human can tell because the partially transparent areas of the image will look wrong.