Vertical shift and lateral shift are phenomena due to refraction of light rays when they travel from one medium into another.
When light rays travel across two parallel surfaces, the emergent rays from the second surface are parallel to the incident rays on the first surface. The perpendicular distance between them is the lateral shift.
A glass slab (paper weight) on a piece of paper, a glass of water on a table, a shallow water pond are examples for vertical shift. The light rays from an object at the bottom of the slab, water glass, or pond are bent at the surface of water or glass and are bent away from the normal at the point of incidence.
So for a viewer an object at the bottom of a denser medium appears to be raised upwards. This is called the vertical shift. It is basically actual depth - apparent depth. It depends on the refractive index of the medium, the actual depth and the angle of viewing the object.