There is an old Chinese/Japanese tale of the Koi (carp) fish which, through its persistence, was able to swim up a waterfall at a point called Dragons Gate. The gods were so impressed with the feat that they rewarded the koi by transforming it into a powerful dragon. The story symbolizes the virtues of persistence and perseverance.
Persistence can be defined as continuance in a course of action in spite of difficulty or opposition. It is an odd sort of character trait in that by itself it could be used positively or negatively. For instance, persisting in an abusive relationship or persisting at the gambling table after incurring huge losses are examples of maladaptive persistence. To quote Lao Tzu "A journey of a thousand miles begins with one step". Very true, but this says nothing as to whether the journey is worth taking in the first place. To decide whether something is worth pursuing takes a different set of tools such as the ability to rationally evaluate a course of action without being emotionally attached to it.
Though persistence can be used in both good and bad ways, it is a necessary trait to have if one is ever to complete tough tasks or reach difficult goals. Most things which are good in life are rife with problems, setbacks, obstacles and disappointments. Without the ability to persevere through hardship, no worthwhile goal could ever be achieved.
It is believed that "persistence becomes easier and more successful with increasing age, at least up to middle adulthood. A stable attention span and tolerance for frustration take time to develop." (1)
The ability to delay gratification is a connected attribute in that it allows one to control immediate impulses in favor of future rewards (see entry on the Marshmallow Test here).
Positive self-esteem is another important connected trait which is imperative if one is to successfully persevere through difficult tasks. You have to believe that you are a competent person and possess the confidence you can succeed if you are to persevere.
Rewards for the expenditure of high effort also play an important role in the development of persistence. When high effort is followed by a reward, the effort becomes less aversive. The more this is repeated, the more likely the individual is to expend high levels of effort in future difficult tasks (learned industriousness). (2)
(1) Character Strengths and Virtues
(2) Industriousness: How it can be learned