Money has a time value. Just ask yourself, would you rather have your paycheck now, or a year from now? Most people would say prefer it now, which shows that a certain amount of money is worth more today than in the future. That's also the reason people take loans. Maybe they could save up for that thing they're going to buy, and ultimately pay less, but it's worth more to them to have it now.
Interest is the way we compensate for the time value of money. It's also a way to make good money, off of people who are eager to get something right away.