A common ancestor within a family would be someone to whom several branches of a family tree can be traced. For example, anyone who can trace a direct family line to someone like Benjamin Franklin would have him as a common ancestor.
In terms of evolution, common ancestry occurs when separate species of animals can be traced back to a different species from which both evolved. A shrew-like creature called Maelestes gobiensis which lived more 70 million years ago is a common ancestor of all mammals, including humans.
The origin of modern humans and their common ancestor is still not fully resolved. One of the main theories is that they came from Africa around 200,000 years ago. A single group of humans began to spread out into the world, taking with it a genetic makeup which links humans today. The genetic variation in humans today is not very diverse, which is supporting evidence for the Out of Africa theory.