Equality is the state of being equal with all other human beings one encounters, politically, socially, and academically. While this may seem obvious, attempts at achieving equality often run into problems because of differing ideas on what it is that should be "equal."
Many of the revolutions in the 18th and 19th centuries focused on political equality. These revolutionaries sought to create states where citizens could meet as equals, not as lord and vassal or colonizer and colonized. However, as the 20th century dawned, many of the newly "equal" people realized how much material inequality still existed. Moreover, their de jure equality did not mean much without being seen as equal to their "betters." This is why many of the movements of the 20th century were more focused on social and economic equality than political equality. (This focus on things other than rights is often known as "egalitarianism".)
In political science, the two concepts of liberty and equality are sometimes seen as antithetical, because too much liberty leads to gross inequalities in wealth, whereas only strong government action can lead to real equality. (Some anarchists contest this idea, believing that full liberty is impossible without full equality and vice versa.)
A contrast is often made between "equality of opportunity" and "equality of outcome" during partisan bickering over "equality".
 Equality and affirmative action
A good case in which different ideas of equality come into conflict is in affirmative action. From the perspective of some, affirmative action is necessary to bring disadvantaged people into equality with advantaged people. Without some kind of support, equality will never happen. For others, however, that very support creates inequality, as people are not being treated the same now. These two conceptions of equality (while using the same term) make discussions of AA very difficult and contentious.