I think it's useful to realize the meaning of "shape" is not the same as in "what is the shape of this object I'm holding." Because we are a part of the universe, "shape" is about how things work (eg, how light moves through the universe), rather than "is the universe a sphere, cube, hypersphere or some other 'shape'."
This question is probably too broad to be answered here. I suggest reading the WikiPedia article on the 'Shape of the Universe'.
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