Pausing to collect oneself and redouble one's efforts.
A form of "idle" practice.
A saw will become dulled over time and use. At some point one must stop to sharpen it in order to make future cuts easier to make.
To "sharpen the saw" is a centering (or perhaps meditation) technique. Sometimes it is the repetition of an already mostly-mastered skill, but not necessarily acted for some goal but instead acted for the act itself. In this case, it is a form of practice. Often, this action is seen in those who are bored or frustrated but don't want to remove themselves from the exposure to their task.
It is self-time.
An author with writer's block who picks up a newspaper in frustration could be seen as "sharpening the saw".
This skill is frequently seen in the actions of the hacker-type. The hacker-type, while they may be seen as obviously (even idly) skilled in a field, they are sometimes distracted to the point of frustration and find themselves slaving at tasks indirectly related to their beloved field.
This is similar to "hacking around", a form of semi-constructive play. It is experimentation and exploration.