Latin Argumentum ad hominem (or simply an ad hominem, meaning "against the man") is an informal logical fallacy where one attacks the person making an argument rather than the reasoning or evidence for it. The problem with an ad hominem argument is that the truth value of many statements is not dependent on the personal characteristics of the utterer of the statement.
Consider:
It may be true that A is a racist or has some other undesirable property, but that is not relevant to whether A is correct about French geography.
In the above example, B is implying that A is wrong because he is a racist.
Sometimes people will assert that they have been the subject of an ad hominem attack, implying that their opponent has committed an ad hominem fallacy. Simply being the subject of a personal attack doesn't mean that you have been the subject of an ad hominem fallacy.
Consider:
In this example, B is not suggesting that A is wrong because he's an idiot. He's suggesting he's an idiot because he should, by dint of being a geography teacher, know that Paris is the capital of France rather than Belgium. B's argument assumes that A is wrong about Paris being the capital of Belgium, but does not conclude that it is wrong on the basis of a personal characteristic. Rather, the causation is reversed: he is concluding with a personal characteristic on the basis of the wrongness of A's statement.
Some writers on informal fallacies have concluded that attributing ad hominem fallacies where they don't exist is another type of informal fallacy.