A given name is a name given to a person at birth or baptism. Given names are referred as first names. It is different from a surname. A surname is the last name or family name.
Example: A baby girl is born and someone decides to name her Hope. Hope is her given name. Someone can decide to give her a surname as it is commonly accepted for people to have a last name. When she grows up, she can pick her own given name or surname if she does not like the one that was picked for her. Family names are inherited and are not easily changed.
In most Western countries the given name comes first (before the last name or family name). However, in many Asian countries such as India's Telugu States, Japan and China it comes after the last name or family name, and occasionally also in Europe, e.g. in Hungarian.
Christians often call their first name their "Christian name".