Basically, without them the output of the converter whether it is voltage or current will be square wave, on/ off. Most of loads can not handle such waves. In order to smooth out the current an inductor is used and to smooth out the voltage a capacitor is used. Therefore, basically the inductor and the capacitor act as a filter.
This square wave, if you analyze it using Fourier, its multiple of cosines and sines with different frequencies added up together to form the square wave. In order to filter the high frequency waves, an LC filter is used.