When you make a mea culpa, you're admitting "I did it. I'm guilty!" It's a way of saying you were wrong.
This is a Latin phrase that simply means "through my fault." So when you make a mea culpa, you're acknowledging that you did something wrong and apologizing for it. This term sounds fancy and official, but it's also a bit of an old-fashioned concept. In a world where people tend to avoid responsibility for their mistakes, it's refreshing to hear someone offer a mea culpa.