I think the quote means that an individual who achieves success through his own abilities, talents, and hard work (own wings) has no limit as to where you can go. I think it also might suggest that this person is free to feel proud of their own success because it is their own. They didn't need to have others carry them on their shoulders, so they can take pride and all the credit for the work that is their own.
Well, it means that one shouldn't go beyond one's abilities. In other words, know your strengths and weaknesses. If you do this you won't find yourself in a fix.