I like this explanation from Pastor Frank Starr:
Some Christians maintain that wrath and punishment is inconsistent with a God of love and mercy. But this view strips God of His holiness, which hates sin and cannot countenance it. God's grace has made a way for us to escape His wrath by providing Jesus as our substitute. On our behalf, the Savior on the cross bore the full weight of God's wrath against our sin.
From Light for the Way, Book 4, page 80