In Logic, ‘fallacy’ is defined as an error in the structure or content of an argument which prevents a conclusion from being rationally drawn from the premises.

An error in an argument.

Fallacies divide into two distinct types:

Formal fallacies occur when a deductive argument is not properly formed. Since validity (a conclusion’s following necessarily from the premises) is determined by the structure of the argument alone, any error in structure causes the argument to fail.

For example:

If Kato is a dog, then he is a mammal.
Kato is a mammal.
Therefore, Kato is a dog.

In this argument the first premise tells us that being a dog is sufficient for being a mammal, but it does not tell us that being a mammal is sufficient for being a dog (there are many other kinds of mammals). So, if we assume that Kato is indeed a mammal, as is asserted in the second premise, we do not have enough information to conclude that he is a dog. This is the fallacy of Affirming the Consequent.

Informal fallacies are much more difficult to spot because they occur, not because of the form or structure of an inductive argument, but rather because we either have insufficient, irrelevant, or ambiguous evidence to warrant the conclusion. Because there are an almost infinite variety of inductive arguments, and because the conclusions of these arguments will only be probably (never certain), there is an almost infinite variety of errors that could occur.

For a more detailed explanation see Informal Fallacy.