The universe is “flat” in a higher dimensional sense. When we think of our existence on Earth, we’re thinking of being 3D beings sitting on the 2D surface of a 3D object.
When physicists talk about the shape of the universe, they’re talking about the experience of sitting on the 3D surface of a 4D object. There is observable curvature in space-time due to black holes and such, but we’ve come to the conclusion that in the absence of gravity or energy, there is no curvature.
Edit: I totally failed at the “explain like I’m 5” part, I’ll admit.
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