In grammar, the subjunctive mood (sometimes referred to as the conjunctive mood) is a verb mood that exists in many languages. It typically expresses wishes, commands (in subordinate clauses), emotion, possibility, judgement, necessity, and statements that are contrary to fact at present. The details of subjunctive use vary from language to language.

Real Life example from Alberto Gonzales interview with NBC's Pete Williams:

I would never have asked for their resignations to interfere with a public corruption case or in any way to interfere with an ongoing investigation.  I just wouldn't do that.  And if you look carefully at the documentations we've provided to Congress, there's no evidence of that.

That's right--he never says he didn't do it. He says he wouldn't. That's not the same thing.

Extra bonus interesting stuff:

Pete Williams: Mr. Attorney General, what is it that you would like people to know about this controversy?

Attorney General Alberto Gonzales: Let me begin with the attacks on my credibility, which really have pained me and my family.  You know, I have grown up — I grew up with nothing but my integrity.  And someday, when I leave this office, I am confident that I will leave with my integrity.  The United States attorneys that were asked — to resign — were appointed by this president, they serve, like me, at the pleasure of the president.

I asked for their resignation not for improper reasons.  I would never have asked for their resignations to interfere with a public corruption case or in any way to interfere with an ongoing investigation. 

Pete Williams never brought up interference with a public corruption case, motherfucker.