In general, magazines are dated ahead to let them stay on the shelves longer and give them a longer selling life.
Let’s say a magazine that hits the stands in February is dated February. When March 1 rolls around, no one is likely to buy it (after all, it’s “last month’s issue”) and the store/newsstand/whatever will probably pull it off the shelf for the same reason.
However, if the same magazine is dated April, it will stay out there another two months giving it more time to be sold.
The purpose of the “display until April 1” note in your link is to tell the store/newsstand/whatever owner to leave the magazine on the shelf until April 1 and not to pull it automatically when the next issue of the magazine comes in.
As for why the April issue “expires” on April 1 instead of April 30, I don’t know. Kind of defeats the purpose of advance dating the magazine in the first place.