In general, the genetic errors responsible for the onset of cancer are somatic mutations, that is they occur in the same somatic cell (liver, pancreas, etc.) that would later become cancerous. Therefore, they usually do not affect germ cell lines and thus cannot be transmitted to future generations. However, in a small number of cases, so called "hereditary", such mutations are structural and can be found in all cells of the patient.
In this scenario, these mutations can be passed down from generation to generation and their presence can be detected in the DNA extracted from a normal blood sample. In such case, the individual has a genome with already built-in errors that highly increase the likelihood of developing cancer. For example, women with a mutation in the BRCA1 gene have a much higher chance of developing breast or ovarian cancer than the rest of the population.
Genes are inherited from both parents. Therefore, if one of the two parents has a inherited genetic mutation, his or her children have a 50% chance to inherit such mutation. Having this mutation in the genome doesn't automatically imply that these individuals will for sure develop cancer during their life. However, they are much more at risk than the rest of the population because their cells have a DNA which is already altered and the road ahead before developing cancer is shorter.