Good answers here, but most are above an eli5. Let me give it a try:
When scientists use the word “flat” they are not saying the universe is flat like a piece of paper. Rather they are implying that (to the best observations we have) it “does not curve”.
To understand this wording we can take a look at our own planet. From our perspective, standing on the ground, the earth seems pretty flat. However, if you starting traveling in a straight line, you would eventually end up back at the same place. Zooming way, way out – you can see why. They earth is actually a sphere and you have walked all the way around the curve.
The larger universe, on the other hand, appears to be “flat”. It you took off in a rocket, you would continue to move away from your original point. You would not “curve” around and end up back where you started.
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