So, for example, modal dispersion can be explained for step index fibres simply by the different individual length of the their zig-zag path ways along the fibre. Even at the same speed of light the arrival time at the end of the fibre will be different and thus the (time) width of an optical pulse in that fibre will be broadened there.
For mono mode fibre there is no modal dispersion. Here the optical pulse dispersion is due to the difference in refractive index seen by the light pulse having a finite optical band width; thus experiencing slight different speeds of light according to the slight differences in the refractice index of the fibre core.