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, consider the case of a hypothetical papal election in which only 100 cardinals vote of the 120 who are eligible. 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 cardinals that can vote, then Cardinal A would not win, since he then would need 80 votes.
In parliamentary procedure, the term two-thirds majority is discouraged as being self-contradictory and confusing, since the word majority always means "more than half". Instead, the term used is "two thirds of those present and voting", "two thirds of those present" (which has the effect of counting abstentions as votes against the proposal) or "two thirds of the entire membership" (also "two thirds of those members duly elected and sworn," in American politics), as appropriate. The term two-thirds vote, if not otherwise qualified, always means "two thirds of those present and voting".
Mason's Manual notes, "A deliberative body cannot by its own act or rule require a two-thirds vote to take any action where the constitution or controlling authority requires only a majority vote. To require a two-thirds vote, for example, to take any action would be to give to any number more than one-third of the members the power to defeat the action and amount to a delegation of the powers of the body to a minority.
In parliamentary procedure, another type of supermajority is a majority of the entire membership that is based on the total number of voting members of the society. It is any number more than one half of the total number of members.
To illustrate, if the society has 35 members a majority of the entire membership is more than 17.5 votes (usually 18, unless there are fractional votes). If only 20 members attend, a motion receiving 17 votes for adoption would not meet this requirement, even if the other 3 members chose not to vote, i.e. abstained.
Some parliamentary authorities, such as Robert's Rules of Order use a majority of the entire member as an alternate method to Rescind or Amend Something Previously Adopted or to adopt special rules of order.
A majority of the fixed membership is a supermajority that is based on the total number of the established fixed membership of the deliberative assembly. It is used only when a specific number of seats or memberships is established in the rules governing the organization, e.g. a board of seven members.
This majority of the fixed members is set at any number greater than one half ot the total possible memberships or seats. For example, on a 7 member board, the majority of the fixed membership is 3.5 (usually 4 votes). For something to receive a majority of the fixed it would have to receive more than 3.5 votes. If the board had 4 vacancies, and only three members remaining, it would be impossible for any motion to receive a majority of the fixed membership, even if all three members voted in favor of it.
Most private organizations do not use this standard. The popular parliamentary manual, Robert's Rules of Order, does not require it for any action. It is sometimes the standard set to adopt some or all actions in state and local government legislative bodies in the United States.
The United States Senate requires a supermajority of 60 percent to move to a vote through a cloture motion, which closes debate on a bill or nomination, thus ending a filibuster by a minority of members. In current practice, the mere threat of a filibuster prevents passing almost any measure that has less than 60 percent agreement in the Senate. There are currently 100 members, so sixty percent is sixty Senators.
The United States Constitution requires a supermajority of two-thirds of both houses of Congress to propose a Congress-driven constitutional amendment; it also requires a three-quarters supermajority of state legislatures for final adoption of any constitutional amendment, a two-thirds supermajority of both houses of Congress to pass a bill over the president's veto, and a majority of the fixed membership to elect a President and Vice President (of Electors in the Electoral College, or if the election should pass to the Congress to decide, a majority of State delegations in the House to elect the President, and a majority of Senators to elect the Vice President).
The Clarity Act in Canada gives the Parliament of Canada the power to decide if a referendum relating to provincial secession has obtained a "clear majority", implying that some sort of supermajority is needed. If it is determined it has not obtained a supermajority, the results of the referendum will be dismissed and the province cannot unilaterally declare independence legally.