Breast cancer is a common cancer – about 1 in 8 women in the UK will get it during their lifetime. If you have just one, or even two, elderly relatives diagnosed with breast cancer, it doesn't mean you are at a much increased risk yourself.
About 5-10% of all breast cancers are thought to be due to a strong hereditary susceptibility. This means that most breast cancers (9 in 10) happen without there being a strong family history of breast cancer.
The two genes most commonly involved in familial breast and ovarian cancer are the BRCA1 and BRCA2 genes (short for breast cancer 1 and breast cancer 2 genes). Although they are called breast cancer genes, they also affect the risk of ovarian cancer. A mutation in another gene, the TP53 gene, is also associated with an increased risk of breast cancer and some other types of cancers at a young age, but this is much rarer.
It's very likely that there are other genes involved in causing a susceptibility to breast cancer, but these haven't been identified yet.