You need a clear understanding of interest rate.
Interest rate is nothing but the opportunity cost of holding money. It is the price you pay for the cash in your wallet. It is the price of present consumption.
Now think a level deeper. You have some cash in your wallet or in your house. What were the other opportunities of using that cash? You would have invested that cash and let's say you would have done a small business and earned a profit.
You plan to keep it in the bank and authorise the bank to use that cash for a stipulated time. Now your bank should compensate you with a part of productivity that your cash would generate. Your cash is actually a capital that earns a return. So rate of interest is nothing but rate of return on your investable cash. If there is no investment there would not be any rate of interest because further value could not be generated without investment.
Now inflation could be controlled by increasing the rate of interest in a closed economy. Higher rate of interest would discourage investor to take loans and invest. Higher rate of interest would also discourage households to hold liquid cash and decrease spending thereby decrease their demand which would exert. a downward pressure on prices.
The higher interest rate never means printing more money instead it means printing less money.
See, the interest rate is nothing but the price of money which is determined from the intersection of money demand and money supply curves. When you increase the money supply that is you print more money you tend to decrease the price of money that is the interest rate and vice verca.
Hope this explanation brings in conceptual clarity.