From Namespedia - Names Meaning and Origins
Meaning: God's promise/God is my vow; noble maiden
Comments: Elsa is a variant of Elizabeth of Scandinavian origin. The popularity of this name grew greatly in the 19th century, owing to the success of Richard Wagner's opera "Lohengrin" (1850), whose (fictional) heroine is Princess Elsa of Brabant. Wagner's heroine is probably the reason why the meaning of this name is often given as 'noble maiden'.