As you see in the third equation on that Mathworks page, the Merton model postulates that the value of equity equals the value on a residual claim on a company's assets after the debtor has been repaid. Economically speaking, equity is a call option on the asset value $A$ with strike price equal to the liability $L$, the formula for which is

$$
E=AN(d_1)-Le^{-rT}N(d_2)
$$

We further note that the volatility of the asset process is (with a bit of *handwaverianism*)

$$\sigma^2\left(\frac{dA_t}{A_t}\right)\equiv \sigma_a^2dt$$

Finally, we know for a call option that $ \frac{\partial E}{\partial A}=N(d_1)$ which is also colloquially called *Delta*. Thus

\begin{align}
E&=AN(d_1)-Le^{-rT}N(d_2) \\
\Rightarrow dE&=N(d_1)dA\\
\Rightarrow \frac{dE}{E}&=\frac{1}{E}N(d_1)dA\\
\Rightarrow \frac{dE}{E}&=\frac{A}{E}N(d_1)\frac{dA}{A}
\end{align}

and ultimately 

$$
\sigma_E\equiv \sigma\left(\frac{dE}{E}\right)=\frac{A}{E}N(d_1)\sigma\left(\frac{dA}{A}\right)=\frac{A}{E}N(d_1)\sigma_A
$$