An easier question to ask might be, "What isn’t algebra?" There's algebra in the money we make, save, and spend; there's algebra in the construction of everything from kitchen sinks to Priuses to skyscrapers; there's algebra in the preparing, baking, and cooking of food; and there's algebra in watching TV. But only if you're attempting to figure out the perfect distance you should be from your television set so that your eyes don’t get all buggy.
Algebra is a branch of pure mathematics that deals with the rules of operations and solving equations. Basically, if you’ve got a few pieces of information and you're looking for one last bit that'll make everything else come together, algebra is there for you. Like Friends.
If you think of all of mathematics as a giant wagon wheel with each branch as a separate spoke, algebra would be the hub. It can be directly applied to just about every other type of math you can think of...and probably quite a few that you can’t. To understand any sort of advanced mathematical concept, in other words, first we've got to wrap our heads around the basics: algebra.
Fortunately, the basics are pretty basic. Imagine that.
To get your feet wet, here's a quick example video of algebra in action.