Why Do Inflation and Interest Rates Have Such a Tangled Relationship?

Imagine you're running a lemonade stand, and everyone wants to buy your lemonade. You raise the price, this is like inflation. Now imagine someone tells you they'll pay more for lemonade later if you promise them better quality next time, this is like interest rates. When inflation is high, people expect prices to go up even more, so banks increase interest rates to slow things down.