Old Time music is from the Appalachian mountains in the United States. Many of the tunes originally came from the UK, particularly Northumberland, Ireland and Scotland. Many tunes from remoter areas in the UK emerged before the 1600s when the major or minor keys became popular; they use other modal keys, giving these tunes a distinctive ancient and raw sound.
The tunes were taken to America by the Scots-Irish between the 1680s and late 1700s, and gradually changed to reflect a new way of life, with new ways of living, places and musical influences. Initially tunes developed for solo dance fiddling in small isolated communities, leading to use of drones and cross-tunings for volume and rhythm. Later they were influenced by cross-cultural music, in particular the rhythmic roots of the African banjo. And over time, solo fiddle tunes developed into string band music, usually including banjo and guitar.
The music was originally just folk music, but was named as Old Time during the era that saw the introduction of recorded music and development of new musical genres such as Bluegrass.
You can explore Old Time music by listening to modern musicians such as Rayna Gellert, Brad Leftwich, Bruce Molsky (who also plays Irish folk), Earl White and Joseph Decosimo. String bands include the lively Foghorn Stringband. You can also listen to old field recordings from the 1920s onwards via the Slippery Hill website, which has early recordings by players such as Tommy Jarrell. YouTube is a valuable learning resource for fiddlers, with slow-downable albums and field recordings, session videos (try looking up Clifftop sessions), and online fiddle and tune tutorials for players of stages and genres.