Fairness is a property of a system or process where no part is privileged, along some measure. A common problem is how to divide a cake between 3 people. Should every one get a third? what if one of them is hungrier? What if they don’t agree about what is fair? This is an example of fair division.
Talking about fairness is difficult, as it runs into many problems with language (as surely the first sentence in this page does). What does privilege mean? what does it mean for someone to be entitled to something?
It also runs it problems of value. How do we measure value? is value objective or subjective? How do we know how much value something is worth to someone? Should an arbiter decide or can people decide between themselves?
Objective value is considered impossible, so objective fairness is considered impossible too. Which means an arbiter can’t be used, and participants have to find a arrangement which is subjectively fair to them.
Which opens up problems of truthfulness, strategy and verification.
Several posts on LessWrong deal with this topic, and it’s also a field of research called Fair Division.