Doc is a wandering Diplodocus (longneck) who goes "where the road takes him." He is shown to be very taciturn and not forthcoming of his past. The Dinosaur Filmography describes his voice as being as gravelly as a bone bed.
Legends in the story
As Grandpa Longneck tells the children at the beginning of The Secret of Saurus Rock, The Lone Dinosaur was a legendary hero long ago - before Grandpa Longneck was alive, as he states later in the movie - who would just show up out of nowhere whenever there was danger afoot in a community. One day, what was declared the "biggest, meanest, most ferocious Sharptooth ever" came to the Great Valley, and while everyone ran away, the Lone Dinosaur appeared and battled with the Sharptooth on his own. His opponent managed to lacerate his eye, which apparently left a permanent scar running down the side of his face, but he emerged victorious.
A short while after he had defeated the Sharptooth and left the Great Valley, a rocky formation rose up out of the ground, shaped like a Longneck, with a ring of teeth encircling its neck. The teeth were said to be those of the same Sharptooth as the one he had killed. It was also believed (and later in the film seems to be proven true) that if the formation got damaged in any way, it would unleash its curse on the entire valley.
Comparisons in the present
Shortly after appearing in the Great Valley, he saved Littlefoot, who quickly went on to idolize the wanderer. Littlefoot believed Doc to be the legendary "Lone Dinosaur", who saved the Great Valley long ago from the most terrible Sharptooth. He based these assumptions on the fact that Doc can do fancy tricks with his tail; that he had been to the Great Valley before; that he has a scar on his eye, and that he has a resemblance to Saurus Rock. Cera, however, pointed out that the legends took place a long time ago, and that the real Lone Dinosaur couldn't still be alive, but Cera than doubts her theory on the speculation.
Role in the show and films
To a degree, after Littlefoot starts idolizing Doc, he places him above his own grandfather and defends him when he is accused of bringing bad luck to the Valley. Towards the end, Doc and Grandpa Longneck work together to save Littlefoot from an Allosaurus and a Tyrannosaurus; Littlefoot asks Doc to stay in case the Valley should ever need a hero; Doc replies that the Valley already has a hero and looks towards Grandpa Longneck. Doc has not appeared in any of the Name Dara subsequent films.