Question

Define lateral displacement on what factors that lead to displacement depends

Answer 1

it depends upon the thickness of the glass slab , the angle of incidence and angle of refraction and since these two angles are related by refracted index so we can say displacement depend upon refracted index

Answer 2

it is the perpendicular shift in the path of the incident ray,while emerging out of a glass block. 
it depends upon the thickness of a medium:higher the thickness more will be its lateral displacement
it depends on the refractive index of material : more refractive index more will be lateral displacement.
it depends on angle of incidence : more the angle of incidence more will be its lateral displacement
it depends on wavelength