What is growing on the flower stem?

Even Cattleya hybrids may occasionally produce an adventitous growth.

A plantlet (called a keiki (kay-kee), the Hawaiian word for baby) will sometimes grow on a flower spike (called an "inflorescence"). Initially small, it will grow several leaves and then roots, at which time it can be removed to propagate a new plant. Once the roots grow a couple of inches long, gently remove the plantlet with a sterile knife and pot in a container to which you add a label with the plant's name. Orchids are susceptible to viruses, so whenever cutting an orchid plant, always use a sterile tool to prevent the spread of virus. With proper care, a keiki may flower in a year. Small keikis could take two or three years to reach flowering size.