What is it called when the newspaper takes back what it printed?

A newspaper will print a retraction if the information they used in an article is proven to be substantially false or inaccurate, especially if the false information will adversely affect a person's reputation or will substantially and unfairly affect public opinion (about an issue, for example).

Example: In a town, two men have the same but unusual first and middle names. Their last names sound alike but are spelled differently, one with 'ea' and one with 'ee' in the name. The one man is a Preacher, a Community Activist, and highly regarded Author who has never been in trouble with the law. The other man also has never been arrested and is a family man, but he got drunk and hit a police car. He was arrested for drunk driving, resisting arrest, and other charges. The newspaper mistakenly identified the law breaker as the Preacher, talking about his prior good community work which implied he no longer deserved that praise. While the drunk man didn't want his bad deed in the newspaper, it is public record. However, the Preacher was greatly concerned that he was mistakenly identified. The newspaper checked the facts, and wrote a retraction which stated the correct information and that the Preacher had been wrongly attributed as being charged by police.

Example: Local elections had a heated race between 3 candidates for Mayor. The newspaper printed financial contributions for all 3, but mixed up the facts. They attributed undocumented campaign contributions to one candidate that was actually about another candidate. The information reflected negatively on the wrongdoer's ethics and ability to lead while following the laws. The wrongly identified candidate insisted the newspaper print a retraction to clear the one guy and name the correct person who was committing campaign fraud.

Newspapers do not have to retract a story just because it names a person or offends, as long as they report facts correctly. A retraction serves to correct false information and often to issue an apology to a person who was wrongly named. But it also must rise to a level that is serious enough to warrant a retraction. For example, a newspaper might correct a name for who won an award, but it isn't as serious enough to warrant a "retraction"---but the paper might include a "Correction". They won't retract "facts" just because a person doesn't like attention to their wrongdoing.