Okay kiddo, let's say you have a piece of paper in front of you. If you hold it with two hands at opposite ends and push down in the middle, the paper will bend, right? Flexural rigidity is how much the paper resists that bending.
Imagine the paper is like a see-saw. One end is on the ground and the other end is up in the air. If you put a heavy rock on the up end, the see-saw won't move very easily. That's because the rock is making the see-saw rigid or strong.
In the same way, something that's flexurally rigid can resist bending or warping. So when you push down on the paper to try to bend it, if it's flexurally rigid, it will push back against you and not bend as easily.
Scientists and engineers use this concept to design things like buildings, bridges, and airplane wings to make sure they are strong enough to resist bending when they are being used.