When interest rates are raised, it becomes more expensive (for individuals, companies, banks, basically everyone) to borrow money. It also means that money kept in savings will receive a higher return.
So in a relatively short period of time, a rise in interest rates can get a country to cut down on spending. And if people aren’t buying stuff, prices will stop increasing (i.e. inflation will slow down) due to lack of demand.
No doubt there is a much more complete explanation to it, but hopefully this provides an intuitive understanding of the basic idea.
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