Plotting $(x^2 + y^2 - 1)^3 - x^2 y^3 = 0$ I have no idea how this equation:
\begin{equation}
    (x^2 + y^2 - 1)^3 - x^2 y^3 = 0
\end{equation}
Produces this picture:

Can someone provide a general explanation of plotting this function?

It's easier to be understood in polar coordinates.
(x^2 + y^2 - 1)^3 - x^2*y^3 == 0 /. {x -> r*Cos[\[Theta]], 
   y -> r*Sin[\[Theta]]} // FullSimplify

% // ApplySides[#/r^5 &, #] &

$$
\left(r^2-1\right)^3=r^5 \sin ^3(\theta ) \cos ^2(\theta ) \\
\frac{\left(r^2-1\right)^3}{r^5}=\sin ^3(\theta ) \cos ^2(\theta )
$$

Plot[Sin[\[Theta]]^3*Cos[\[Theta]]^2, {\[Theta], 0, 2 Pi}]


Plot[(r^2 - 1)^3/r^5, {r, 0, 5}]


