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 teh 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 agebra, 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 balloons.

Why Do I Need Algebra?
Only you can answer this question. I've always said 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.

Ultimately, you need to do your own homework to determine if your goals mean sticking it out in math, however, you can never go wrong if you do.