BruceMB, a medical biologist once explained this a little. There is always the possibility of some normal cells becoming cancerous, which means they start multiplying with no regard to proper function. These are the cells cancer treatments try to kill. With smoking, or any other cancer promoting substance, the chances of cells becoming cancerous rises. Some people are also more prone to having cells become cancerous (sometimes specific organs, thus genetic determinants in breast cancer, for example). Some people are less prone to having cells become cancerous, and you may add to that the luck of the draw: none of your grandfather's cells happened to become cancerous, due to good genes and the laws of chance.

As to the other deletorious effects of smoking, like respiratory ailments, they are real enough. I've seen a full-on asthma attack occur in a woman too polite to tell the visiting smoker in her own home to butt out.