How does general confession work when ordinary confession absolves you of all your past sins?

During confession, if I mention (in passing or in reference to) a sin I've committed in the distant past, the priest usually asks if I had confessed it before. If I say yes, he says it has been absolved and I don't have to confess it again. What is the difference between a general confession and a regular confession if past sins that have been absolved need not be confessed again?