It presumably evokes occasional and unpredictably extreme rainfall in Appalachia that has historically isolated rural neighborhoods and interrupted travel.
[1] The earliest documented appearance in print is the 1851 use of the phrase "Providence permittin’, and the creek don’t rise" by an uneducated but highly expressive female character in a short story in Graham's Magazine.
[2] The expression experienced a rise in popularity in the second half of the 20th century due to its use by Tennessee Ernie Ford as the sign-off for his television shows.
[4][2] Classic versions of its use tend to be along the lines of "The good Lord willing, and the creek doesn't rise"—i.e.
It may take the form of regional dialect, in variations like "... Lor' willin' an' th' crick don' rise."