When the Federal Reserve sells treasury bonds to a bank, the money supply is decreased. Since there are smaller available funds for the bank to loan (they have tied up some cash by buying the bonds), the interest rate the bank charges (all other things EQUAL!) will increase.
Basically, what has happened is that the bank has lent money to the federal government, rather than to other lenders. So if it has no other sources of lendable funds AND borrowers don't have other banks to go to that are charging the current rate, the same number of borrowers competing for a smaller amount of borrowable funds will lead to a higher price, (interest rate) for those loans.