When you confess, you admit to doing something wrong. You might feel guilty about eating the entire platter of chocolate chip cookies and confess to your mom before she notices. If she presses charges, you would confess to the cookie crime.
Confess can be used to describe admitting to committing a crime. If you watch crime shows on TV, you've likely seen detectives trying to get a suspect to confess. Confess can also be used in a religious context. Catholics confess their sins to a priest on a regular basis. Don't confuse the word confess with apology. An apology involves expressing regret about something. When you confess, you're merely owning up to doing it — you might not be sorry.