Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing).
This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.
Most of us have borrowed to buy something. Credit cards, in particular, can be quite convenient (but dangerous if not used in moderation).
This tutorial explains credit card interest, how credit card companies make money and a far more silly way of borrowing money called "payday" loans.
If you gladly pay for a hamburger on Tuesday for a hamburger today, is it equivalent to paying for it today?
A reasonable argument can be made that most everything in finance really boils down to "present value". So pay attention to this tutorial.
Back in the day (like medieval Europe), you would actually be thrown in jail if you couldn't pay your debts (debtor's prison). That seemed like a pretty awful thing to do (not to mention that lenders are much less likely to be paid by someone rotting in prison), so governments created an "out" called bankruptcy (which, as you'll see, is a pseudo-painful "reset" button on your finances).