Confession in a time of worship is simply an expression of our ongoing need for God’s forgiveness. It’s our admission of our sins and failures to love, the recognition that we don’t come before God because of our holiness or purity, but because of God’s forgiveness and love. Confessing our sins together is an important reminder that we aren’t finished yet, it’s a reflection of the "not yet" part of the already/not-yet tension of the Kingdom.
For the first thousand years of Christian worship, confession was actually not part of the worship time itself, but was done beforehand. The liturgical prayer of confession didn’t come until later (11th century), and consisted in a mutual confession of sin by both priest and people.
Where you put confession in a liturgy is a bit up in the air. To confess sin before adoration reflects, for example, Psalm 24 ("Who may ascend the hill of the Lord? He who has clean hands and a pure heart"). But to adore before confessing sin reflects Isaiah 6, where Isaiah first saw God glorified, then confessed his sin.
Confession of sin ought also to be both personal and corporate, and speak of sins against God and against our fellow human beings. It’s also important to recognize that when a local Body of Christ confesses their sins together, they are not simply isolated individuals who come together to confess their individual sins, but they as an alive Body confess their sins together. We are linked together with others in the Body of Christ in a symbiotic relationship, where my supposedly "private" sin actually does have ramifications for the entire congregation I worship with. Just like Achan’s sin had consequences for the whole nation of Israel, the sin of even one member affects the whole Body. So it is important to confess our sins together, with this in mind.
After the confession there should always be a statement of absolution, or forgiveness. Since confession is both a corporate and an individual act, the statement of absolution is also a corporate and individual speech-act: my personal sins are forgiven, and the corporate sins of this Body of Christ are forgiven as well. While the "cross is the basis of forgiveness, … the actual forgiveness comes from God’s proclamation: ‘Your sins are forgiven’" (Chan).
We need to hear God’s word of forgiveness just as much as we need to confess our sins. We learn that forgiveness is a relational idea – forgiveness re-establishes the relationship that sin had severed. As we engage regularly in this element of worship, the rhythm of confession and absolution gets into our veins and we begin to live out forgiveness in the rest of our lives, re-establishing human relationships that have been severed through sin.