The circuit of the full wave bridge rectifier is below:
The smoothing capacitor is being connected across the load and reduces ripple in the rectified output signal by charging and discharging. It accumulates electrical energy in the electric field between its plates when the voltage accross the capacitor is higher than the capacitor's one and discharges the accumulated energy through the load when the voltage on the output of the rectifier is lower than the voltage stored by the capacitor's plates. Thus when there is no voltage in the rectifier, there is voltage that the capacitor gives away and the signal looks like that:
The blue voltage is a rectified voltage without the smoothing capacitor, the green one - with the capacitor. The more the capacity - the less the ripple. The same about the load: small load resistance may not influence ripple, but high load resistance lessens the ripple because it decreases the time constant.