The most important invention in the last 2000 years has to be the moveable-type printing press. Cheap book production put the printed language in the hands of the masses and led directly to the rise of literacy. Once you have a large literate class, you see the democratic impulse flourish — even a moderately educated populace begins to make judgments about its rulers and its mode of government. Cheap book production also advances both scientific and historical knowledge by ensuring that valuable source documents are duplicated and preserved and (just as important, really) ensuring that those old documents are readable. Cheap book duplication makes it possible to quickly build a cadre of scientists and historians who've read the same works and thus share a common body of knowledge. Finally, moveable type makes it possible for the past to speak to the future en masse in a way that the evanescent oral tradition never could.
It's helpful to look at the other inventions listed as the most important in the last 2000 years and try to imagine how they might have come about had there been no moveable-type printing press.