Brown soap doesn't seem like it would be all that desirable. Unfortunately, in some cases it's not something that the soap maker has any real control over.
Many things affect the color of soap. The most common (and drastic) of these is vanilla content in the fragrance used to scent the soap. Vanilla, or vanillin, typically causes soaps to turn brown over time. The percentage of vanillin in a particular fragrance oil directly effects the amount of color change. Fragrances with low levels of vanillin will not change much, while fragrances with high levels will turn a dark chocolate brown over time. This generally happens during the 4-6 week cure period, so the colors of the soaps you see in my store should be their final colors.
Because fragrance oils are proprietary to their makers, there is no real way to know precisely how much of any one component is in each one. However, most soap fragrance suppliers give a percentage of vanilla. As you use them more, you are able to predict fairly accurately how dark your soap will get over time. Most overly "sweet" scents tend to have high levels of vanilla, as well as bakery type scents. When using fragrances will high vanilla levels, keep in mind that the soap will turn a dark brown.
For example, in the soap listed above, the vanilla content is listed at 11.5%, and this is reflected in the very dark color of the finished soap. The purple was achieved by leaving that portion unscented. Over time, the brown color may migrate into the purple section, or they may stay separate. This does not affect the soap in any way other than aesthetics.