What does 'confess your faults' mean in the Bible?

It means to face up to the fact that you have specific faults and to acknowledge to God (and yourself) the particular times when you have done something wrong.

The Word "confess" only means "acknowledge" and does not actually require the idea of "repent", but it is clear from the context that people who confess their faults will also repent of them.

Therefore the implication is that people who "confess" a fault will commit not to make that mistake again.