If the treatment for the original tumour leaves even one cell alive that cell can keep on surviving in the body. If it finds a welcoming spot in the body – one where it has access to a blood supply and can evade the immune system – it can keep growing and dividing into two daughter cells, repeating the process until it eventually seeds a whole new tumour in a new location.
For breast cancer, the new location is often the bone, liver, or brain – other cancer types will spread to other locations. This phenomenon is seen in many different types of cancer, not just breast. The disease can seem to reappear after such a long time because it can take a very long time for the cell to create a new tumour that’s big enough to cause symptoms or show up in medical scans. The cells that develop resistance to chemotherapy drugs aren’t always the ones that grow the fastest – in fact, it might be in part a slow growth rate that protects them from the effects of the drug. So the cell was there all along; it just wasn’t noticed.