Location of Erebor or The Lonely Mountain in relation to the Iron Hills, Ered Mithrin (Grey Mountains), Mirkwood and The Misty Mountains. (Click to enlarge and then zoom in).
In the first chapter of The Hobbit, "An Unexpected Party", Thorin talks about his memories of the Erebor of his youth. He was 24 in dwarf years when Smaug invaded Erebor - this is young for a dwarf. He describes himself as "only a lad" when that happened. Consider that a dwarf is only deemed "battle ready" when they are over 30 (Wikipedia) and they generally marry at around 100 years (Tolkien Gateway). Their average life expectancy is 250 years! That is about 3 to 4 times our average life expectancy as human beings. Therefore, when Thorin meets Bilbo, he may be 195 years old in dwarf years but if we can hypothetically equate that in "human years", he would have been the equivalent of about late 40's/early 50s in maturity. (So ..... to counter the arguments I have read on other sites that RA is too young to play Thorin, going by my calculations, the make up department just has to age him about 10 (+) years. We know from the story that he is fit and very capable of fighting.)
Erebor as it was before Smaug.
Here is Thorin's description of Erebor as he knew it as a child. (from Ch 1, The Hobbit)
"Long ago in my grandfather Thrór's time our family was driven out of the Far North, and came back with all their wealth and their tools to this Mountain on the map. It had been discovered by my far ancestor, Thráin the Old, but now they mined and they tunnelled and they made huger halls and greater workshops - and in addition they found a good deal of gold and a great many jewels too. Anyway they grew immediately rich and famous, and my grandfather was King under the Mountain again, and treated with great reverence by the mortal men, who lived to the South, and were gradually spreading up the Running River as far as the valley overshadowed by the Mountain. They built the merry town of Dale there in those days. Kings used to send for our smiths and reward even the least skilful most richly ........ Altogether those were good days for us, and the poorest of us had money to spend and to lend, and leisure to make beautiful things ...... So my grandfather's halls became full of armour and jewels and carvings and cups, and the toy market of Dale was the wonder of the North." (J.R.R. Tolkien. "The Hobbit")
Later, in a chapter called, "Inside Information", Thorin describes the heirloom of the line od Durin - the Arkenstone ...
"....... But fairest of all was the great white gem which the dwarves had found under The Mountain, the Heart of the Mountain, the Arkenstone of Thrain.'The Arkenstone! the Arkenstone!' murmured Thorin in the dark, half dreaming with his chin upon his knees.'It was like a globe with a thousand faces; it shone like silver in the firelight, like water in the sun, like snow under the stars, like rain upon the Moon!" (J.R.R. Tolkien, "The Hobbit")
The Arkenstone had great significance for the descendants of Thráin 1 and for Thorin. It signified the Heart of the Mountain and was one of the dwarves most prized possessions. The Arkenstone was a means by which Thorin could reconnect with his ancestors, and establish himself as a great leader. It was lost to the dwarves when Smaug sacked Erebor in 2770 when Thorin was still very young. The desire to find it was perhaps central to Thorin's quest to reclaim Erebor.