In the context of events on the farm, any association with what is deemed human is immensely symbolic. In his speech before the rebellion, Old Major made it a point of denouncing the adoption of human characteristics. When he addressed the animals in the big barn, he expostulated in part:
And remember also that in fighting against Man, we must not come to resemble him. Even when you have conquered him, do not adopt his vices. No animal must ever live in a house, or sleep in a bed, or wear clothes, or drink alcohol, or smoke tobacco, or touch money, or engage in trade. All the habits of Man are evil.
This was an emphatic warning against the evils of man. Adopting his habits meant that one has identified with whatever man represents. Old Major's advice was incorporated as one of the main ideas of the principles of Animalism and written into the seven commandments:
No animal shall wear clothes.
No animal shall sleep in a bed.
No animal shall drink alcohol.
The animals initially strictly adhered to these, as seen in Snowball's admonition to Mollie when she asked about wearing ribbons:
“Comrade,” said Snowball, “those ribbons that you are so devoted to are the badge of slavery. Can you not understand that liberty is worth more than ribbons?”
Therefore, once the pigs started wearing green ribbons on their tails on Sundays, it firstly, signified their rejection of the principles of Animalism. Secondly, they had adopted the human traits that Old Major had warned about which implies that they deemed themselves more human than animal. This, in itself, further suggests that they saw themselves the superior of the other animals. The idea of equality did not, therefore, resonate with them.
In addition, since the pigs were accepted as the brain workers on the farm and they, as a consequence, did not perform any manual labour, it was logical for them to assume that they were better. Wearing ribbons on their tails was, therefore, an expression of this. The ribbons also clearly indicated their position of authority since the privilege was extended to them only.
Furthermore, the situation on the farm had reached a point where the pigs had already broken and altered a number of the other commandments. They had moved into the farmhouse and slept in beds. Napoleon had proceeded to wear Mr Jones' clothes and his favorite sow was wearing Mrs Jones' dresses.
Added to that, Napoleon had assumed the role of Leader and was addressed as such. This happened shortly after he had brutally executed a number of animals for purportedly having betrayed their comrades by secretly helping the demonized and banished Snowball in his attempts to overthrow the farm.
The general animal populace was now in a constant state of fear and apprehension, too afraid to speak out or challenge what was being done. They were easily mislead and manipulated by Squealer's lies. In the process, they had been enslaved by their own kind and the pigs had free rein to do as they pleased.
In the final analysis then, the ribbons become the most pertinent and emphatic symbol of the pigs' dominance. They are better than the other animals and deserve their subservience. They have come to epitomise the new single commandment:
All animals are equal but some animals are more equal than others.
Early in the book, one of the tenants of Animalism is that no animal should wear clothing, since that is a human trait and humans are bad. This includes decorative ribbons, which the horses sometimes wear on Market Day, and Boxer's straw hat which keeps the flies out of his ears. However, it becomes clear that the pigs are becoming more rulers and less equal citizens.
About this time, too, it was laid down as a rule that when a pig and any other animal met on the path, the other animal must stand aside: and also that all pigs, of whatever degree, were to have the privilege of wearing green ribbons on their tails on Sundays.
(Orwell, Animal Farm, msxnet.org)
The pigs, in slowly creating their superiority over the other animals, have already begun to adopt human characteristics, such as living in the farmhouse and sleeping in beds. The green ribbons, the color of the Animal Farm flag, serve as a reminder to the other animals that the pigs are superior and more worthy of respect, and that they should be obeyed without question. They act as a mark of "otherness," separating the working-class animals from the elite-class pigs.