B Flat Universe: What Does It Mean to be 3-Dimensional?

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This may be a very trivial question. I would like to know how a universe could be flat if we are 3 dimensional. When i think of "flat" i think of something similar to a sheet of paper. Although technically 3 dimensional, the paper looks pretty 2 dimensional. So how is 3 dimensional space time "flat"?
 
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Flat in this context means not curved. That is, the geometry of space is such that angles in all triangles add up to 180 degrees, all circles have circumferences equal to 2πr, and all parallel lines stay parallel.
 
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