On a log-log plot of surface gravity to planet mass, what is the meaning of the y-intercept?
For planets of constant mean density you have:
$$
M=\rho \times 4\pi r^3
$$
and the surface value of $g$ is:
$$
g(r)=\frac{GM}{r^2}=G \times \rho\times 4 \pi \times r
$$
So for bodies of constant density the surface gravity is proportional to the radius, and the slope as $r \to 0$ tells you the density. So for bodies of equal density $\log(g(r)) \to -\infty$ as $r \to 0$

In terms of mass:
$$
g(M)={G(4\pi \rho)^{2/3}M^{1/3}}
$$ 
So as $M\to 0$ we have $g(M)\to 0$ and again $\log(g(M))\to -\infty$ and the intercept of the $\log-\log$ plot as $M$ goes to zero alows you to calculate the mean density.