A galvanic cell is a spontaneous cell.  By supplying an outside electro source to a non-spontaneous cell we can force a reaction to occur.  An electrolytic cell is one in which a non-spontaneous reaction is induced to occur.
A external power source acts as an electron pump to supply an "over-voltage" of electrons to cause the transfer of electrons inside the cell.  An over-voltage is required since supplying just enough voltage to over come the negative cell potential still only brings the cell potential to zero (0 V).  The over-voltage takes it into the +ve region and hence makes it spontaneous.