After his conversation with Smaug, Bilbo was worried and uncomfortable because he had inadvertently revealed information about the people of Lake-town to the dragon, putting them in danger. He was also concerned that Smaug would attack Lake-town.
Balin comforted him by praising his bravery and resourcefulness, reminding him of the important role he had to play in their quest.
Bilbo's worry and discomfort stemmed from his realization that he had endangered the people of Lake-town by inadvertently revealing information to Smaug. This is evident from the fact that he urged the dwarves to move to the safety of the tunnel and was concerned about Smaug's potential attack on Lake-town
Balin comforted Bilbo by praising his bravery and resourcefulness, highlighting the important role he had to play in their quest. This is in line with Balin's character, as he was known for his wisdom and kindness towards Bilbo throughout the sto