What is a down pillow insert?

A down pillow insert could be one of two things:

Within the industry it would generally mean the cardboard insert that goes inside the packaging. Most pillows arrive in a bag which has a pocket on the inside - we generally call the cardboard that goes inside this an insert.

The only other thing I can think of is that it could possibly be another name for a down surround pillow. This pillow is for people who feel that a goose down pillow is not supportive enough for them. It has a feather filling on the inside which is essentially inside a small pillow - this is then covered with down so that you have the softness of down but the support of feather.