Although the whole person concept generally does not factor into an initial application -- there, your application, submitted materials, references, and investigation results control -- it does play an important role in appealing a denial or revocation of a clearance. Basically, if some detrimental information or disqualifying incident pops up, which would otherwise deny you clearance, positive factors may be taken into account to overcome the presumption of disqualification.
Essentially, there are two types of positive factors that can help you. The first includes factors that mitigate the seriousness of negative conduct. For example, if your background reveals that you have been convicted of shoplifting, this could result in disqualification and denial of a clearance. But if you can demonstrate that you paid full restitution to the store, were only 19 years old at the time, played only a minor role in the incident, and the conviction was set aside by the judge after you completed your probation early, then the effect of the conviction may be minimized, and your application may be approved.
The second type of positive "whole person" factor includes anything that demonstrates your trustworthiness, diligence, dedication to the community or country, or overall good character. These factors can indirectly minimize the negative impact of a black mark on your record. Things like participation in civic, charitable, religious, or educational organizations can demonstrate good character and involvement in the community. Awards and achievements for excellent job or academic performance can show your diligence and trustworthiness. Recommendations from distinguished and highly-regarded professionals can bolster your character. Basically, produce anything that gives an affirmative answer to the question, "Can we trust this person?"
While it is better to avoid any blemishes on your record, having evidence to demonstrate that a black mark is an anomaly, and not a personality characteristic, will help you. Thus, if you want your future to include work that requires scrutiny of your past, you should take action to burnish your present. Besides, it just feels good to do something positive!