Quick explanation
All the matter in the Universe causes the Universe itself to have a geometry which may be different from what you might believe.
That means that the geometric rules we're used to — e.g. that a triangle has 180°, and that parallel lines never meet — may not be exactly true.
That's pretty hard to imagine in a three-dimensional space, but a good analogy is to think of a two-dimensional surface such as a table top; here the usual rules are valid. But a two-dimensional surface can also be curved, like the surface of a ball. Here, triangles have more than 180°, and lines starting out parallel eventually meet.
Besides just wanting to know what kind of universe we live in (like it's nice to know whether the Earth is flat or round), the geometry of the Universe also impacts astronomical observations, so if we want to understand what we see, we have to know the geometry.
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