The federal reserve rate is essentially how much the US pay's their debtors. Bank's use this as a benchmark for how much they lend to their own borrowers.
The inflation rate is a calculation done based on a basket of goods. if the price of that basket of goods goes up, inflation is up. if it goes down, inflation is down.
When the federal reserve lowers their rates, it makes it easier to get money, and therefore the price of the basket of goods goes up.
When they make their rates higher, money is harder to get, and the price of the basket of goods goes down. The only problem with this is that there is also less money for labor, which means that unemployment goes up. The Feds job is to balance these two things.