The legend is that at some point during the 1780s the Reverend Elijah Craig, a baptist minister and distiller who had been incarcerated earlier in his career when his sermons were deemed to be causing a breach of the peace, suffered a fire at his distillery which damaged many of his barrels.
Being too stingy to replace them, he filled the burnt barrels with whiskey regardless, noticing later that the whiskey from the burnt barrels tasted better. It's most likely a myth, but it's a good one.
While this may or may not be true, it seems unlikely that this was the genesis of bourbon, as the Rev. Craig's distillery was never located in Bourbon county, and at the time there were likely hundreds of similar spirit-distillers in operation in the state. Nonetheless, Reverend Craig has become a symbol of the pioneer spirit in Kentucky folklore, and today his place in bourbon history is honoured by the Heaven Hill company, who produce two very popular long-aged small batch whiskeys bearing his name.