The authors of the study hypothesize that a possible explanation for the inverse relationship between the organic food consumption and a reduced risk of cancer is the decrease of contaminants such as pesticides.
Well, it has been suggested that people who eat organic food are inclined to have a healthier lifestyle and habits which could in some way lower cancer risk. Although the presently the study is not conclusive nonetheless studies have demonstrated a correlation between organic food consumption and pesticide levels in urine.
In the meantime, eating more fruit and vegetables, regardless of organic or non-organic, less red meat, less processed food, and exercise regularly is the way to go.
For more details of the study please read HERE.