Basically, it involves leaving family money and identity behind and going one's own way, creating an identity based solely on personal achievements.
Henry Clay is credited with coining the phrase, "self-made man," in a speech made before the Senate on February 2, 1832. "In Kentucky, almost every manufactory known to me, is in the hands of enterprising and self-made men, who have acquired whatever wealth they possess by patient and diligent labor." The OED even claims this to be the first use of the term.
However, in further study, I found an article by a gentleman, SubtropicBob, who disputes this. He googled that great online research tool, newspaperarchive.com and found a print article--a letter signed by a Professor Newman--about Roger Sherman, Declaration signer and . . . self made man! Professor Newman claimed that Sherman rose from humble beginnings, etc. And--he wrote this letter to the Delaware Advertiser on October 9, 1828, predating the Clay quote by 5 years.
Who cares? SubtropicBob and I. I have changed my References and Endnotes, as well as the text of First Fallen, to reflect this new information.
It never hurts to keep researching.