The veil of ignorance is a term used to refer to a particular idea that conveys that we should always be excellent to each other. The veil of ignorance is itself a thought experiment; it describes how one should mould one's political stance in order to assist those who are not yourself.
Suppose that before one was born, one took a certain spirit form, unknowing of one's future. Suppose indeed that this was true of every human who would ever live; before Time took form, before the first elements were so far from each other as the Planck length, suppose there was a massive council of all spirits. Suppose this was a perfect democracy - there was no Time, and so there was no Entropy, and so there was no Hunger, and so the council could consult each member with patience and respect for the lack of Time that each person had to their name. For Time, they knew, was in the Future, which they knew as what was after the council.
Suppose that before one was born, one's spirit form knew not what body it would assume. Perhaps a pre-historic Neanderthal woman; perhaps an African tribesman during 17th century Colonialism; perhaps a genderqueer individual born 15 years before the onset of the Singularity; perhaps a modern Chinese factory worker with a wife and two children; perhaps a cancer patient who grew up in rural Georgia, USA; perhaps a disabled veteran of a draft...
Suppose that one had the perfect lack of Time - for Time was without substance, and so incomprehensible - and that one had the perfect lack of Life - for Life comes with Culture, with Belief, with Knowledge - and suppose that one stripped away all of this world, leaving only the universal moral principles. Perhaps one believes in equality, and in maximum total good - perhaps in other ideals like justice and hope.
Or not. The exact universal moral principles one believes to be true don't matter for the experiment. The thought experiment demonstrates how you behave, and measures whether you live up to them.
Suppose you were to be one of these spirits. You know not which side of Colonialism you'll end up on (technically, neither would you know that it would happen; but someone may have brought a similar idea to you as a thought experiment, to demonstrate their case). Neither do you know whether you'll be genderqueer, or how research toward friendly AI will be practiced, or whether you'll work under Chinese or American safety standards -
- but, and here is the crucial piece of the thought experiment, you will be in charge of determining your fate. And that, perhaps, is terrifying. You and the likely-to-be-uncountably-vast democracy are in charge of determining the laws under which the world will operate.
It's assumed that together, you will determine certain values. There are only so many resources in the world, and expending too many resources on pursuing exact equality will leave everyone poor (and probably lead to everyone's death (but that's OK, everyone who will ever live is here, right? so everyone is in this together? ... probably?)). At the same time, leaving runaway economic inequality to its own devices is probably not the sort of lottery moat of those present wants to bet on. Remember, money is only correlated with happiness until one reaches the middle class.
The veil of ignorance is as follows: Suppose we were ignorant of the role we would take in life, and yet were imbued with the education and ability to make decisions that we currently have. In this case, what political stance would you take? How much would you choose to donate to charity (in time, research, and money)? What job would you choose to take? How would you behave toward others?
Vote for your caring, trustworthy president.