Each caste in Aldous Huxley's Brave New World is distinguished by the color of its work clothes. In order of caste from lowest to highest, Epsilons dress in black, Deltas wear khaki, Gammas wear leaf green, Betas dress in mulberry, and Alphas wear grey.
This color division system to differentiate castes is in place so that people can quickly and easily know what caste a person is in. The dystopian world described in Huxley's novel is very superficial, so of course they would use a superficial designation like color coding. It is surface-level symbolism, but also very effective psychologically. The world is also one that relies heavily on simplistic psychological conditioning, as seen with the Pavlovian type conditioning and the electric shocks.
In such a world, it is incredibly important to know at all times who is in which caste, which the color system perpetuates and concretizes. It is vital for the continuation of the oppressive state because the caste system is the absolute most powerful tool the dystopian government, the World State, has to oppress and brainwash their citizens. Using genetic modification techniques, the World State makes the lower castes physically unable to rebel. In their fetal state, they are introduced to alcohol in their blood, deprived of oxygen, and then afterwards they must undergo extreme brainwashing and conditioning. Thus, lower class citizens are created to be servile and lesser. It is in their "nature," as manipulated as it is. This system allows for the dominance of certain people over others, and the systematic nature of the oppression makes it extremely difficult to challenge. In fact, one could argue that it's even impossible to challenge based on the way in which the oppression has taken root. So although it seems arbitrary, the color system in the World State castes is actually an incredibly systematic way of keeping the status quo.