Bilbo talks to Smaug who unwittingly coughs up that despite the impenetrable scales has a weak spot near his heart.
Bilbo first encounters Smaug when he creeps down the tiny side passage into the Lonely Mountain and steals a golden cup from Smaug's stack while the dragon is sleeping.
Bilbo creeps down the passage a second time to see if he can find some kind of weak point in Smaug's armor. This time, Smaug is awake. Luckily, Bilbo's ring of invisibility gives him some safety. And Smaug wants to find out where Bilbo is from, so he doesn't kill him outright.
The two fall into conversation. Smaug asks Bilbo's name. Bilbo doesn't want to give Smaug his name for fear of evil spells, but he also doesn't want to refuse Smaug's request for fear of angering the dragon (neither would we). So Bilbo calls himself a number of fancy names – "Barrel-rider" being the primary one. Bilbo tells Smaug that he isn't here for money; he and his friends have come for revenge. Smaug laughs at the very idea. He turns over to show off the magnificence of his scales. He thinks no weapon will be able to hurt him. But Smaug is unaware of an unscaled patch on his chest: a weak spot! Bilbo creeps off, and Smaug sends a wave of flame after him. Bilbo barely escapes unburned.
Smaug is a "most especially greedy, strong, and wicked" dragon who comes flying out of the North to attack the Lonely Mountain a couple of generations before The Hobbit takes place. Read more about Smaug's character and the summary of "The Hobbit, or, There and Back Again" at Shmoop.