The larger circle has center $O$ and passes through $D$. The smaller circle has diameter $OD$. What percent of the larger circle's area is gray?

[asy]import graph;
draw(Circle((0,0),30),black);
fill(Circle((0,-15),15),gray(.6));
draw(Circle((0,-15),15),black);
draw((0,0)--(0,-30),black);
label("O",(0,0),N);
label("D",(0,-30),S);
[/asy]
The ratio of the radius of the smaller circle to that of the larger circle is $\frac{1}{2}$, since the diameter is half as long.  Thus, the ratio of the area of the smaller circle to that of the larger circle is $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$.  Thus, the gray area is $\boxed{25\%}$ of the area of the larger circle.

To be more rigorous: if the radius of the larger circle is $r$, the radius of the smaller circle is $\frac{1}{2} r$.  Thus, the ratio of the area of the smaller to the larger is: $\frac{\pi (\frac{1}{2} r)^2}{\pi r^2} = \frac{1}{4}$.