A confession is an admission of guilt, fault, or a mistake.
You’ve probably seen TV shows or movies where a detective says to a suspect "Confess!" The detective is trying to get a confession, which is a statement that admits some type of guilt. "I killed the mayor!" is a confession. "I forgot your birthday" is a confession. In some religions, confession is a sacrament where people admit their sins and seek forgiveness. When people have something painful to admit, they often start by saying, "I have a confession to make."