Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. (computing) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.
 adj. Said of an element of an algebraic structure (such as a group or semigroup) with a binary operation: that when the element operates on itself, the result is equal to itself.
 adj. Said of a binary operation: that all of the distinct elements it can operate on are idempotent (in the sense given just above).
 n. An idempotent ring or other structure
from The Century Dictionary and Cyclopedia
 n. In multiple algebra, a quantity which multiplied into itself gives itself. Ordinary unity is idempotent.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. unchanged in value following multiplication by itself
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

On your last few paragraphs, I'm not sure I get your comment about it being "idempotent" with creationist second law arguments  though I can't say I'm terribly familiar with those.

My first instinct would be to stop using the pretentious word "idempotent"

My first instinct would be to stop using the pretentious word "idempotent", which is a symptom of the Haskellers 'disease of assuming that math terminology is a good way to concisely communicate concepts to nonmathematicians ...

The act of providing information is idempotent, at least from the perspective of the user; any sideeffects of a CARBON request are the responsibility of the entity that handles them, just like with an HTTP GET request.

A together with • and Â·, along with 0 and 1, forms a ring with identity in which every element is idempotent.

These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent.

His fascination with the possibilities of ordinary algebra led him to consider questions such as: What would logic be like if the idempotent law were replaced by the law X3 = X?

As mentioned earlier, Boole gave inadequate sets of equational axioms for his system, originally starting with the two laws due to Gregory plus his idempotent law; these were accompanied by De Morgan's inference rule that one could carry out the same operation

He was interested in the structure of rings of linear operators and realized that the central idempotents, that is, the operators E that commuted with all other operators in the ring under multiplication (that is, EL = LE for all L in the ring) and which were idempotent under multiplication

For example, as long as the arguments satisfy the relevant condition Î¾, Ã— is idempotent, commutative, and associative, and it interacts with + in conformity with the the following distribution laws:
john commented on the word idempotent
"An idempotent operation in math is one that has the same effect whether you apply it once, or more than once. Multiplying a number by zero is idempotent: 4 x 0 x 0 x 0 is the same as 4 x 0."
 "RESTful Web Services," pg. 102.
August 24, 2007