What is Algebra?
Simply put, Algebra is about finding the unknown or it is about putting real life problems into equations and then solving them. Unfortunately many textbooks go straight to the rules, procedures and formulas, forgetting that these are real life problems being solved. A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors etc.
In the simplest of form, I could say:
A clown was carrying a handful of balloons. Along came the wind and blew 8 away, leaving him only with 9. How many did he start with?
In algebra, this problem would then be converted to: x - 8 = 9
The x replaces the unknown that we are trying to find out, we know the wind blew 8 away and we know that the man was left with 9 balloons.
Remember, in Algebra x seems to be the favorite letter to substitute for the unknown.
The goal in algebra is to find out the unknown. Therefore, we often end up with x = something. In this problem, when you apply algebra, you'll learn that it's like using a scale, you want to isolate x and in so doing you'll do the same thing on each side of the = sign. To isolate x in x-8=9, I will need to add 8 to the left side of the = sign and add 8 to the right side of the = sign. I am then left with x = 8 + 9 therefore solving my real life problem that x = 17, meaning that the balloon man started with 17
Why Take Algebra?
Since algebra is "putting real life problems into equations and then solving them" and "finding the unknown", then clearly algebra is a good life skill to have. It is used in every day life to figure out how long it will take to get to your destination, what grade you will get in class based on how well you do on homework and tests, how much food to serve at a party, and how much money you will make based on the number of hours you work. It is used by people in many professions such as carpenters, electricians, architects, and computer scientists.
It is also the foundation to other higher level math classes. So just like learning addition, subtraction, multiplication, and division; it is important to have a good understanding of algebra before learning other higher level math concepts.
As stated in About.Com "math is an opportunity gateway and you can't get to higher maths without taking algebra. Algebra develops your thinking, specifically logic, patterns, problem solving, deductive and inductive reasoning. The more math you have, the greater the opportunity for jobs in engineering, actuary, physics, programming, etc. Higher math is often an important requirement for entrance to college or universities."
Above and Beyond (Optional)
Here are some interesting topics that you may be interested in.
Origins of Algebra - Where did the word "Algebra" and its underlying ideas come from
The Beautify of Algebra - Why the abstraction of mathematics is so fundamental.