Inflation is a result of too much $$$ chasing too few goods. So, by raising interest rates it (hopefully) dampens the demand, because many things are purchased on credit. In effect, the cost of credit would reduce demand, and reduced buying would hopefully then force suppliers to lower their prices to move their inventories.
Lower prices would seem to encourage cash buyers; because they don't have to pay the extra cost for credit. But raising interest rates also gives people with cash an incentive to save rather than buy.
For a good example, look at what rising mortgage rates are are doing to the cost of real estate. With the higher interest rates, fewer people can afford to buy a home, and with reduced demand, home prices should come down.
But all of the above is chancy and may backfire because there's much more to it. Like inflation also causes employees to demand more from there employers, and higher interest rates also affect corporate borrowing. Also a lot of business and consumer credit is variable and raising interest rates on existing credit can push somme consumers and businesses over the edge. This happened just 12 or 15 years ago, and it looks like it may soon be happening again.
