From Academic Kids
A two-thirds majority is a common supermajoritarian requirement in elections, especially whenever minority rights can be changed (e.g. constitutional amendments). There are two kinds of two-thirds majority: the simple or the absolute. The term is a corruption of the proper term (used in Robert's Rules of Order) - a two-thirds vote.
A two-thirds majority means that the number of votes for a proposition or candidate must equal or exceed twice the number of votes against it. If unqualified, two-thirds majority by itself always means simple two-thirds majority.
As an example, let's take the case of a hypothetical papal election. At this hypothetical conclave, only 100 cardinals vote of the 120 that can vote. The results are that Cardinal A had 67 votes, Cardinal B had 20 votes, and Cardinal C had 13 votes. Cardinal A in this case has a simple two-thirds majority.
An absolute two-thirds majority means that two-thirds of the entire membership of a body or more must agree to the proposition. It is much stronger than a simple requirement. In the above case, if it required an absolute two-thirds majority of the 120 cardials that can vote, then Cardinal A would not win, since he then would need 80 votes.