In the science-fiction short story "Harrison Bergeron" by Kurt Vonnegut Jr., equality for all people is imposed by government mandate. Because people are inherently dissimilar, attractive people have to wear masks, strong people have to wear weights, and intelligent people are beset by periodic noises to keep them from thinking too much. Although at the beginning of the story Vonnegut writes that people are "equal every which way," it is obviously not true, because then Harrison's rebellion would not have been necessary, and the government would not have had to quell it by force.
To speculate on complete equality poses numerous questions. How could this be achieved? Would genetic manipulation be used? Would it be necessary to eliminate disparities of physical appearance and expertise such as skin color, strength, abilities, and gender? Regardless of the details, a completely equal society would provide numerous advantages. We'll delineate a few of these, and then you can choose the two you feel would be most relevant.
Complete equality would bring an end to envy and jealousy. These emotions are predicated on inequality. We envy other people because they have more than we do. However, if everyone is equal and everyone has exactly the same advantages and talents, people would have no motivation to feel these negative emotions.
There would be no bullying and violence in a society in which people are completely equal. Bullies are motivated from feelings of inferiority. They think that they will enhance their own self-esteem by dominating, ridiculing, and physically abusing others. People fight each other to prove their superiority, but when everyone is equal, this is no longer necessary. In a larger sense, inequalities provoke wars between nations, when one nation has resources or advantages that another wants. When there is complete equality, there would be no more fighting or wars.
If people are completely equal, everyone would respect one another because they would be exactly the same. There would be no more racism, sexism, or other negative evaluations and treatment of fellow humans.
In a society of equals, there would presumably be a mutual sharing of resources. Nobody would have too much, and everyone would have enough. After all, if everyone is just like you, you would want to see that their needs are taken care of.