A gene is a specific segment of DNA that determines a specific cell function. Genes control things like eye color, hair color, height and size. An example group of genes that are important to cancer development is the tumor suppressor genes. Such genes control the growth of a cell and its ability to repair itself if it is changed by a mutation (perhaps from an environmental insult). If a tumor suppressor gene mutates and is no longer able to stop the cell from uncontrolled growth then that cell give rise to the development of cancer.
There are hundreds of thousands of genes controlling all processes in the body. Genes are passed down through the generations. Some cancers are partly inherited (BRCA1 and BRCA2 breast and ovarian cancer), but most involve spontaneous or "sporadic" mutation in an individual due to faulty suppressor gene function, environmental insult and other factors.

Many cancers are "graded" according to what they look like under the microscope. If the cancer retains the appearance of the normal structure from which it arose, then it is called well differentiated, or Grade I. If it is difficult to determine the structure of origin, then it is called poorly differentiated or Grade III. Moderately differentiated or Grade II cancers are in between. Clinically, Grade I cancers tend to behave better and are less aggressive than Grade III, which tends to behave the worst. Grade II is in between.