The science of TTF was developed by Dr. Yorum Palti, a professor emeritus of physiology and biophysics at the Technion – Israel Institute of Technology. Since Dr. Palti’s pioneering work demonstrating the effects of tumor treating fields at reducing solid cancer tumors over 15 years ago, there have been over 20 peer-reviewed articles on the science of TTF.

While the understanding of the mechanism of action behind TTF is still evolving, the latest compelling research comes from a study conducted by Kenneth D. Swanson, Ph.D, of the Harvard School of Medicine in Boston, Massachusetts. 

In summary and in layman's terms, specially tuned TTFs are sent through cancer cells during cell division. The TTFs interact with charged particles within the cells that are dipole. That is, they are positive on one side and negative on the other. These particles move back and forth with the alternating electric field (the TTF). This prevents them from functioning normally.

Cells that complete division under the influence of TTF are damaged and show signs of distress

Dr Kenneth Swanson's full scientific presentation via YouTube: 

Evidence suggests that the distressed nature of cancer cells that divide under TTF triggers an immune response, which kills the cells and causes tumor reduction.