The American Declaration of Independence claimed that "all men are created equal.'
The real meaning of equality is that people are 'equal' because we have fundamentally similar characteristics, because we are human beings, with rights and obligations common to all. Another way of saying this might be to say that all people are entitled to the same respect for their dignity, that we are all born with, whatever our status or circumstances. Justice is a form of equality.
Another sense of equality is not individual at all. There are rich countries, and poor: some with an abundance of natural resources, and others with very few. There are developed, and developing countries, and the state of their development affects individuals' life chances. There are, in other words, two kinds of equality - personal, and developmental. Human rights means ensuring that there are, at least, equal chances.
Everyone is 'equal' in status, but every one is a different and unique individual. We all have a similar capacity for feeling pain and pleasure, anticipation and dread. We all make moral decisions. We can use our reason to guide our lives, choices and our relationships. We all have the same right to be treated with respect, even when we make mistakes. We all have the same measure of innate worth.
Equality of opportunity means giving very different - unequal - people an equal chance. It means that everyone must be given an equal opportunity to achieve the same outcomes. We do have unequal social positions. Some people are disadvantaged by circumstances of birth, others by the society they grew up in, or by their experiences. We all have different talents, but should have the same choice on how we realise them.
Some say 'equal opportunity' laws undermine human freedom by preventing people with advantage from exploiting it. This is a 'liberal' equality view: that we should leave people equally free to pursue their 'chosen' course, without taking their environmental or circumstantial disadvantages into account. Would this be 'just'? Is this 'equality'? As Anatole France said, 'the majestic equality of the law ...forbids the rich as well as the poor to steal bread and to sleep under bridges.'
Equality means no more nor less than the right to equal consideration. Since the world is not 'fair', it means removing artificial barriers to achieving and choosing. After all, if 'all men are created equal,' why do women keep missing out?
United Nations High Commissioner for Human Rights
Human Rights and Equal Opportunity Commission of Australia