If inflation is the target of a central bank, why would one increase interest rates?
If interest rate is higher then it is more expensive to borrow thus people less able to get easy money to purchase goods and services. It reduces aggregate demand preventing price level from old growth.
But it is only demand-side effect. Here is also supply-side effect of such policy if it used without discrimination or untargeted way (firms due to higher interest rates invest less and it may lead to fall in domestic supply etc.)
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Interest rates are set by supply and demand just like every other price in the market. However the fed can lower rates by increasing the supply of money available for loans, but they do this with created money. They can also withdraw money from the system by reversing the process and cause rates to increase. Since the price level is a function of the amount of money in the system and the amount of goods, their actions affect the price level, that is the inflation rate.