You learned from the woman Andraste that the Lord of the Nazgûl was travelling to a place called Othrongroth. If you could spy on the Witch-king at this place, you might learn more of his plans.
'The Great Barrow is not a place for weak hearts or frail limbs. Wicked wights and evil lords make merry in their terror. They've never caught Old Tom and never will they. He's the Master!
'If you be a-going, Tom will take you!'
Tom Bombadil has agreed to show you the way to Othrongroth, a barrow in the Barrow-downs.
Return to Tom Bombadil and claim your reward.
You and your allies braved the dark depths of Othrongroth and emerged victorious.