The world is round, but the universe is flat. I never quite liked this word choice when describing the shape of our universe. We know that there is curvature of spacetime according to Einstein's equations, but over the massive scale, physicists believe that the universe is flat.
Their definition does not necessarily mean 2-dimensional flat, which might cause some confusion. We mean that parallel lines in our universe stay parallel. They wouldn't bend inwards like in a closed universe or diverge like in an open hyperbolic-shaped universe. Scientists believe this is so due to the cosmic microwave background (CMB) which is the remnants in the sky from the big bang.
Gif from Giphy
By analyzing the slight variations in temperature from this radiation, scientists have reason to believe that the universe is flat (or very nearly so). This isn't so much of a bad thing, but it does cause philosophers and theoretical physicists to think about the ultimate fate in such a universe.