When interest rates are increased, borrowing money becomes more expensive. This translates into both individuals and buisnesses having to slow down their enconomic growth, because financing their activities or production also becomes more expensive.
The Federal Reserve has the double-task of keeping prices manageable in a flourishing economy while keeping unemployment as low as possible. When there's inflation, it's been proven that slowing down the economy by increasing interest rates, tends to reduce inflation. That's why it's a good option. We have to keep in mind, however, that this will raise unemployment as a collateral effect.
As you can see, there's no easy answer when it comes to balancing all factors at the same time.
Hope this helps!