Success is often in the eye of the beholder. While one person may think success is establishing a Fortune 500 company, another may simply be content by doing their absolute best at answering phones and filing for a boss their entire career.
A practical example would be my career. Starting a large family while young, I did not set out purposely to become a teacher, nor did I ever think I would be qualified. Yet an opportunity presented itself and, while always looking for a challenge, I jumped at it.
The next eleven years were met with long days and late nights. Classes filled with behaviorally-challenged, hormonal, and often economically disadvantaged youth. While I had awesome colleagues and mentors to turn to for guidance, I still had to establish my own unique learning environment and was responsible for the educational outcome of so many. I embraced the philosophy that if a student fails, I've failed. So I worked even harder when that happened.
In my fifth year, due to the economic decline, I was pink-slipped. The following year I was one of very few whose lay-offs were rescinded. Annually, my course-offerings - and thereby my preparations and huge learning curve - changed drastically in order to serve the needs of the students.
The busy-ness continues with attendance, grading papers, entering grades, tutoring, and following up with parent phone calls for the purpose of both discipline issues and praise reports. Not to mention, since my program is project-based, there are always factors beyond our control and events that consume an enormous amount of time outside the scheduled day.
Yet with all this busy-ness and all of these challenges, I am "interrupted" with a correspondence, a note of appreciation, a token of affection, or a warm hug from a student whose life somehow I managed to enrich and influence... just as he or she ventures out after graduation to achieve his or her dream of success.
I think that this quote is talking about how successful people are often too busy completing tasks and making a difference to worry about the status of their success.
For instance, if a CEO of a company is in the middle of running a company and trying to make sure that the company is making money, the CEO is not likely to be thinking about the success that others will be judging him/her on. Instead, the CEO is focused on the task at hand or the several tasks that the job forces him to do.
Another example can be anyone who is motivated to truly live life. If you are busy doing, you can't spend time worrying. The more you do, the more likely you are to succeed. So by the shear nature of doing, one would be likely to focused on what is in front of them and not the likely success that will come despite looking for it. Those who do look for success aren't being productive enough to find it. I have an uncle who is constantly switching jobs looking for the next best thing instead of just working hard at whatever he's doing. He doesn't like hard work and wants get rich quick schemes. Anyone in this circumstance is NOT likely to find the success they desire.