Sic is a Latin word which means "so" or "thus." It is often used in print to indicate that something has been reproduced accurately, especially in transcripts. When used in print, this word is usually placed in brackets, like this: [sic]. The use of brackets indicates that the word is not part of the original quote or material being printed, but rather that it was added. Brackets are also sometimes used for corrections.
One common use of sic is in reproductions of text with weird spellings. Spelling in the English language is still not widely standardized, with some spellings seeming peculiar to people in some places while they are totally normal in others. The word is also used in reproductions or transcripts of old printed material; the Constitution of the United States, for example, contains a number of things which look like spelling and grammar errors to modern readers, although they were perfectly acceptable at the time.
Many publications use sic in a somewhat snide way, to highlight an error. For example, a newspaper might say: "Jones stated in his book that 'its [sic] unlikely that we will see a change in this policy,'" rather than simply correcting the mistake. A quote like this can also be a case for brackets, which would be used like this: "Jones states in his book that '[it's] unlikely that we will see a change in this policy.'" In both cases, the seemingly innocent brackets draw attention to a common grammatical error, implying to the reader that Jones is perhaps not a totally reliable authority.
Sic is often used in verbatim transcripts of speeches or in quotes from other printed material. The use of the word alerts readers to the fact that the apparent error is simply being reproduced, and it is not the fault of the publisher. Many authors pride themselves on reporting things as they are said, errors and all, and their publications are often littered with this term.
In addition to sic, some publishers also use the term "queer but correct" or "qc" in much the same way, indicating that although something looks wrong, it really isn't. Qc is often used by editors while marking up text for the compositor, to ensure that these errors are not corrected by overzealous typesetters.
There are all sorts of fun ways to use [sic] in text, especially if you happen to be quoting someone you don't particularly like, as an appearance of [sic] in a quote carries all sorts of implications. For example, when a politician says something remarkably stupid, adding a [sic] to the quote when it is printed can be one way of illustrating the stupidity without openly commenting on it. The use of [sic] for ridicule is quite common, and Latin geeks often get a kick out of it.