When there's an inequality, something is out of balance and things are not equal. An inequality occurs in math when the two quantities are not the same measure or amount.
In society, an inequality occurs when rights and privileges are not applied fairly. The civil rights movement in the 1950s and 60s, for example, arose because of inequalities between the races. Blacks in the South could not sit in the front of the bus, drink from the same water fountains as whites, or even attend the same schools. People protested this inequality in many ways, including bus strikes, sit-ins, and marches.