The 'F' rating is short for the 'Fujita' rating of tornados. Dr. Theodore Fujita was an atmospheric scientist at the University of Chicago who did pioneering work into the study of tornados. Traditionally, it has been difficult or impossible to directly measure the wind speeds inside tornados...because they rarely hit official weather stations....and when they do they generally destroy the instruments before an accurate wind speed can be measured.
Dr. Fujita and his fellow scientists developed a method for estimating the wind speeds based upon the degree and extent of damage that the tornados cause. Trained meteorologists will survey the path of a tornado....studying damage to structures, vegetation, vehicles, etc. Using this information they will come up with an 'Fujita', or 'F' rating to describe the strength of the tornado: 'F-1, F-2, etc. Frequently a tornado will strengthen or weaken as it moves along its path...so that a single tornado may change from an 'F-2' to an 'F-3' and back to an 'F-2' for example.