Raising interest rates is raising the cost of borrowing. If people borrow less in reaction to that, they buy less. This means demand falls. So if demand falls, then assuming supply remains steady, prices should fall. Mind you, it’s not the ONLY factor, but it’s a big one.
Raising interest rates is neither inherently good or bad for the economy. It’s more like that it helps some people and hurts others. It’s helpful in some situations and harmful in others. It’s very contextual.
There are many economists who would argue that a steady rate of moderate inflation is good for the economy. This is because inflation encourages people to spend rather than save. When people spend, businesses have incentive to supply goods, and therefore keep hiring. The usual target is 2%. These folks regard deflation, even SMALL amount of deflation, as being very bad.
However, there are others (albeit a minority at this moment in history) who argue that inflation OR deflation are both bad and we should be trying to get as close to monetary stability as we can. This is because discouraging people from saving traps them in a state of relative poverty. Saving creates money to invest, capital to spend on education or other things they might want to improve their station or that of their loved ones. The poor tend to be less savvy investors so if the value of their cash is always declining by 2%, they are less capable of making that up by seeking higher returns like a rich person can.
If the value of money is stable, people can save, and businesses can make more rational investment decisions resulting in less waste that needs to be gutted and a smaller boom/bust cycle. But again, the prevailing wisdom right now is pro-small-amounts-of-inflation. The stability group are largely locked out of policy groups like the Fed.