The Literal meaning is "He shall surely die". The Halachic meaning finds significance in the doubling of the word as is interpreted in Sanhedrin 45b as if the specified form of the death penalty cannot be performed, then any other form can be done.
Regarding meaning this world and the next, on the drash level, I saw that in the Akeidas Yitzchak but I can't remember whereAkeidas Yitzchak by Rabbi Yitzchak Ben Moshe Arama (a late Rishon). Likkutei Levi Yitzchak by Rabbi Levi Yitzchak Schneerson brings that idea as well. But that is more on the drasha level.