The Magic Railroad is a magical railway run by the magic engine, Lady, who in fact brings magic to everything on the island.
The Magic Railroad is, in a way, a bridge between the universes of Shining Time Station and the Island of Sodor. Mr. Conductor and his family are in charge of this mystical line, and their source for gold dust is obtained through the proper running of the line. The land which the railroad runs through is colourful, bright, and of course magical. The tracks are a golden colour. Lady is a key player in the magic, for she recharges the line's magical energy. Without her, the line became a dark, vineyard-like place, with a forest of thorns. Only when Lady finally returned did the line regain its brightness. If Lady had never returned, the line would have eventually faded out of existence, bringing both universes into extreme disorder.
Mr. Conductor and his family use the line as a means of tranportation, and as a way to obtain more gold dust. Travel to either universes would have been impossible without gold dust or the lost engine.
The magic buffers, which are at each end of the line, are key players as well. Finding them on the Island of Sodor wasn't easy, but only when a coal truck went missing did Thomas discover where they were. To use them requires magic or an engine. To use them, Thomas had to charge at them without stopping in order to pass through to the Magic Railroad. An interesting side effect of an inanimate object touching it, such as a tumbleweed, gives the object some intelligence, and the ability to talk.
The buffers at the other end of the line are linked to Muffle Mountain, home to Lady's workshop and Burnett Stone. It is here the line takes a surprising twist, hurtling down the mountain, across a field, and then suddenly diving into another set of buffers. Billy Twofeather's map of the Indian Valley shows several mysterious shadowy lines, like straight railroad tracks, heading towards other places. These are indicated to be part of the Magic Railroad, so it can be assumed that the line branches off into either other universes or other parts of Indian Valley.
Lady's workshop is where Lady is stored when not in use. Burnett Stone can make repairs here, and the tracks leading out are obviously another buffer connection to the Magic Railroad.