Nothing succeeds like success.
This proverb means that success breeds further success. When someone achieves success in one area, it often leads to more opportunities and successes in other areas. Success can be contagious and inspiring, motivating others to work harder and achieve their own successes.
According to Gregory Titelman's America's Popular Proverbs and Sayings, this very American expression originated in France (“Rien ne réussit comme le succès”) with the earliest known use appearing in AngePitou (1854) a book by Alexander Dumas, also known as Storming the Bastille or Six Years Later. Dumas is better known as the author of The Count of Monte Cristo and The Three Musketeers.
But a reference at Google Books points to an 1837 edition of the magazine Revue des deux Mondes that quotes French author M. Jules Janin saying this some years earlier.