English Meaning: The name Amber is an English baby name. In English the meaning of the name Amber is: A jewel name that became popular in the 19th century, from the name of the yellowish resin used in jewellery-making.Used regularly since the publication of 2Oth century writer Kathleen Winsor's novel 'Forever Amber.'.rabic Meaning: The name Amber is an Arabic baby name. In Arabic the meaning of the name Amber is: Jewel. A jewel-quality fossilized resin; as a color the name refers to a warm honey shade.