This is a helpful comment for understanding the significance of the resurrection, especially as it relates to the atonement:
[T]he Gospels…all agree that when the question was put to Jesus, “Are you the Messiah?” he did not deny it. It is in the context of those last days in Jerusalem that the royal title emerges publicly as a potential estimate of Jesus. On the basis of such a possibility, Jesus was executed as a messianic pretender. And for that reason his resurrection can be understood as God’s vindication of the crucified Messiah.
This from Donald Juel, Messianic Exegesis: Christological Interpretation of the Old Testament in Early Christianity (Philadelphia: Fortress, 1988), 26.
See also 1 Corinthians 15 for more on the vindication theme.