The word "algebra" is named after the Arabic word "al-jabr," which comes from the book ”The Compendious Book on Calculation by Completion and Balancing” written by Muslim mathematician Muhammad Al-Khwarizmi. The book, written in 830 CE, explains "Al-jabr" or algebra to mean completion, or subtracting a number from both sides of an equation.
Source: http://www.britannica.com/EBchecked/topic/317171/al-Khwarizmi
