If you read anything about personal finances, you've probably heard about a little thing called compound interest. I want to keep this short and sweet, because I don't doubt that you're an intelligent person who won't have any trouble understanding how it works.
Basically, interest is "rent" paid on money. So, if you lend your cousin $20, and he pays you back $21, you just got $1 in interest. There are two basic types of interest, simple and compound. With simple interest, you pay only on the principle. So if you borrow $100, at 1% interest, you pay back $101.
Things get a little more complicated with compound interest. In this case, you have to pay interest on any interest that was added to the principle. So, if you borrow $100, at 1% interest compounded monthly, and you have to have it all paid back in a year, the total would be $101. If you noticed, that's the same as the first example. That's because compound interest takes time. Let's try the example again, with the same interest rate, but over a longer period of time.
With simple interest, if you had to pay back $100 plus 1% interest, after 30 years the total would be $101. With compound interest, if you had to pay back $100 plus 1% interest, compounded monthly for 30 years the total would be $134.97. It's not major, but with higher interest rates (and they ARE higher), and larger principles the differences can get pretty major. If you want to give it a shot on your own, try this handy calculator I found.
So where does the "magic" part of compound interest come in? Well, ideally you're the one getting compound interest instead of the one paying it. If you're still paying something off, I suggest you finish, then start trying to get someone to pay you instead.
The "magic" is what happens after a long period of time with a pretty reasonable rate and a bigger principle. In a hypothetical situation, let's say I invest $12,000 a year (it's hypothetical because I invest twice that) at around 8% interest compounded daily (like most stocks are) for let's say, 40 years, then at the end of that 40 years I'll have a total of $3,529,362.86. Not bad for only twelve grand a year I'd say.