In Greek, "meta" means change, "morph" means shape, and "magus" (which is latin) means magic or wizard. Therefore putting all the words together the translation is a magic being that can change shape.
A Metamorphmagus known as Metamorphmagi is a witch or sometimes a wizard who has the ability to change their physical appearance at their own will. They do not need potions or spells to do this. It is an extremely rare quality. In this series Sophia Dimitrov has access to this power.
Metamorphmagi are able to take various different forms, for example they can change both their sex and age. This enables them to look like anyone they desire to look like. If this is not what they desire then they can even change a simple part of their features such as eye color. However when this ability is used it is usually used for more than this. Due to this being a rare power Metamorphmagus is a power that is within when you are born. You can not be trained to have this power and you cannot take this power away from someone else.
A more concise summary along with other powers for Witches and Warlocks can be found Powers and Abilities: Witches and Warlocks here.