Mathematical explanation:
The y axis is the value, the x axis the interest rate. Since the value is always the present value of some future cash flows, the formula for is always something like
V = CF_1 / (1 + i) + CF_2 / (1 + i)^2 …
That kind of curve is convex (that is, you take any two points on the curve and connect them, and the resulting line will be above the curve)…
That translates the fact that decreasing the interest rate from 3% to 2% will make the bond price rise more than if you start at 4% and decrease to 3%. Meaning the curve gets steeper and steeper as the interest rate approaches zero.
There’s no deeper reason - it’s just that when you compute the PVs of the future CFs for varying interest rates, and you draw up the curve, it just happens to be a convex one.