The British scientists first created normal embryos from the sperm of a man and egg of a woman (as per usual). However, the woman’s egg contained defective mitochondrial DNA.

Humans inherit their mitochondria only from our mother. So, in order to “fix” the defective mtDNA, the researchers transplanted the existing embryo into an egg with no nuclear DNA (no genome) that had been donated from a second woman who had healthy mitochondria (BBC 2008).
Inherited Mitochondrial Mutations

Inherited changes in mitochondrial DNA (those passed on through the egg of the mother) can cause problems relating to growth, development, and function of the body's systems. These mutations disrupt the mitochondria’s ability to generate ATP energy, and often involve multiple organ systems, particularly organs and tissues that require more energy (such as the heart, brain, and muscles). This new research may be a way of circumventing some of these devastating genetic disorders (National Library of Medicine).