One morning, Angus Cullen sat down to breakfast and began reading the newspaper. The paper featured a story of a horrible murder that had been committed the night before, and described the police's efforts to find the killer. Angus turned to his wife, Sarah, and declare d"I can tell you one thing - this murderer is not a Scotsman. No Scotsman would commit such an act!"
The next day, the papers describe yet another murder, and Angus once again assures Sarah that this fiend is clearly not a Scotsman. But the day after that, the murderer has been caught int he act, and it is none other than Ian MacDonald, born and raised in Edinburgh. Angus looks to Sarah and declares "Edinburgh or no, this murderer is not a true Scotsman!"
The "No true Scotsman" fallacy is a weird sort of logical fallacy in that it seeks not specifically to falsely establish a particular claim, but rather to remove a particular set of actions or views from a group to which those actions and views belong. Probably the most common variation that we see in the U.S. is people claiming that someone is not really a member of a given religion. For example, when you hear someone talking about gay rights, it is very common to hear someone who takes a stand different than the speakers (whether pro or con) dismissed as "not a real Christian", likewise there are many people who will insist that suicide bombers in the Middle East are "not true Muslims."
Newsflash for all y'all - REAL Christians do disagree on social issues. Real Christians work to take care of the poor, while other real Christians do things that make the poor's lot in life even worse. Real Muslims work towards peace, while other real Muslims blow people and property up as part of political terrorism. Real Jews support the Israeli state in all that it does, while other real Jews think that the Israeli government is run by know-nothing thugs. And so on and so forth.
While this is most common, at least in the U.S., among religions, you can also see it in other venues. I remember, during the 2008 presidential primaries, hearing a number of people announce that John McCain was not a real Republican because he often voted against Bush's policies - the irony here being that, in those cases, McCain was usually voting along with what the party's stated platform and traditions actually are.
The "not true Scotsman" fallacy seems to function to allow people to discredit others without ever actually engaging in what they are saying. When someone says "I oppose Proposition X, because I am a member of Group Y", having it pointed out that many members of Group Y support Proposition X runs the risk of making the person making proclamations actually have to give a bit more thought to their position (and perhaps admit that it is their own position and not something that has the full weight and support of Group Y behind it) and this can be scary - so it's much easier to simply deny that the people who disagree are also members of Group Y no matter how absurd such a position may be.