A wrongful conviction is when a person who is innocent is convicted of a crime. Wrongful convictions are typically only discovered after the conviction has been made, and upon further investigation.
Wrongful convictions occur because the criminal justice system is not 100% accurate, and trials do not always lead to perfect justice. This is why, on rare occasions, an innocent defendant may lose the trial and be held responsible for a crime that they didn't commit.
The use of DNA evidence has led to the discovery of many wrongful convictions. As a result, many of these convictions have been overturned. In the past, DNA evidence did not exist, and so it could not be used to prove a defendant's guilt or innocence.
There is an organization called the Innocence Project that is dedicated to identifying innocent incarcerated people, helping them prove their innocence, and overturning their sentences. DNA evidence is commonly used in such efforts.