This phrase is derived from chapter 5 of the Big Book, 'Those who do not recover are people who cannot or will not completely give themselves to this simple program, usually men and women who are constitutionally incapable of being honest with themselves.' AA is a simple program for complicated people, so the saying goes.
AA's Twelve Step program is simple because it works simply: one Step at a time and one day at a time. Simplicity in this sense, does not necessarily mean ease. Working the program requires an unwavering dedicated effort. Yet all the strength and willingness to work the program is freely give to all those who sincerely ask for them.