The word 'algebra' comes from the Arabic "al jabr," which translates roughly as "the reunion of broken parts." An Arabian mathematician wrote a book 1200 years ago which used the term, the title of which translated something like "the science of restoring what is missing and equating like with like." This expression comes down to us as "solving for X."
Our current culture is the beneficiary of science and technology, all of which is explainable mathematically. Although few of us use that level of math on a regular daily basis, algebra, as one branch of mathematics, is important for the resolution of scientific and technical issues. For non-scientists and technicians, the benefit of its study comes from the development of the logic and reason the student must encounter in finding solutions. A student may never do another problem after finishing an Algebra course, but reasoning skills learned are important for anyone considering him or herself a thinking individual.
American Heritage Dictionary
It is a branch from mathematics, where it consist mostly of operations and also equations, terms, polynomials and graphs etc. The word "algebra" can be traced back to the past, where it is found to be a root form of a Arabic language, al-jabr, which means "restoration of something". Algebra is something like reducing or balancing a mathematical equation, meaning the cancellation of like terms from both side of the equation to reduce it into a solvable equation, like a linear or a quadratic equation. Algebra has been proven by many book publications made by famous mathematicians around the world and the famous of it all was the Arithmetica, written by Diophantus, in 3 AD, an Alexandrian mathematician, dubbed the "Father of Algebra". I think Algebra is very useful as it helps you to think logically and clearly and helps you to break down steps into simple methods to solve and verify, good to help you solve problems.