The *realest* reality is the reality of the Ideal Forms 
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To Plato, the grubby real world is below (and mostly dark) whereas the world of Ideal Forms is above (and in the light).
Platonism is built in to Western intellectual culture, so we're inclined to think abstractions are somehow better (or more *real*) than concreteness. The Idea of a Giraffe matters more – and is much more worthy of thought – than any particular giraffe.