Expected short-term interest rates influence long-term rates because any investor has the choice of holding either a long-term security or a series of short-term securities, re-investing his or her funds in a new short-term security as the old short-term security matures. All else being equal, the choice between the two strategies depends on the expected return.
If, on the one hand, short-term rates are expected to be higher on average than the long-term rate that spans the same period, investors will choose the strategy of rolling over short-term securities. If, on the other hand, the long-term rate exceeds the average of expected future short-term rates, the long-term security will be the more attractive.