Prices are a function of balance of supply of goods and services with demand; and balancing the supply of circulating dollars with demand for dollars.
The strategy of increasing interest rates is to contractdict inflation with deflation:
Fiscal - The intent of increasing interest rates to fight inflation is to dimish demand by slowing/reducing economic activity. Reduced demand may result in more surplus goods and services, thus, putting pressure on suppliers to reduce prices.
Monetary - Also, increasing rates is hoped to fight inflation by reducing the number of dollars in circulation. In economics, scarcity creates value. By making the number of circulating dollars more scarce, the intent is to increase the buying power of each remaining dollar (aka, deflation).
One unknown variable beyond the control of the Fed is the velocity of money - how quickly the same dollar changes hands in the facilitation of commerce - through the economy. Spending a dollar is inflationary because spending puts more dollars in circulation. Saving a dollar is deflationary because saving takes that dollar out of circulation.
Another way the Fed can manipulate the number of dollars in circulation (used for spending) is to increase or decrease bank reserves (the cash banks are required to keep on hand for withdrawal). Increasing bank reserve requirements reduces the number of dollars in circulation (deflation). Decreasing bank reserve requirements increases the number of dollars in circulation (inflation).
Rates are as low because the Fed decided that greatest threat from the 2008 financial crisis was deflation - fewer dollars in circulation; fewer dollars available for spending and lending; assets used for loan collateral decrease in dollar value, possibly making the loans insolvent; insufficient supply of dollars in circulation drives up interest rates (the cost of borrowing money) which reduce economic activity (recession, depression). Since 2008, the Fed has pursued inflationary monetary policy to keep a floor under the economy. Now, inflation is a greater economic threat than deflation, so, the Fed is reversing direction to now reduce the number of dollars in circulation.