Refer to figures.
Lateral stability is the tendency for an aircraft to roll away from sideslip. When viewed from above, sideslip is the angle between the nose of the aircraft and the relative wind. It occurs when we are flying “sideways” through the air, either due to an uncoordinated turn, the use of the rudder, or a disturbance (turbulence or gusts).

The dihedral effect describes lateral stability characteristics of an aeroplane, due to wing dihedral. This is when the wings (when viewed from the front) are angled slightly upwards. The result is that when subjected to some sideslip angle, the upwind wing will experience a greater angle of attack (AoA). It will produce more lift, thus rolling the aircraft away from the sideslip. Lateral stability due to dihedral therefore creates roll, which reduces the sideslip angle. 

The objective of designing an aircraft with lateral stability is to return the wings to level, in the event that a disturbance causes a small unintended angle of bank to develop. With no control inputs, and zero sideslip, the wings should be level.

Note: It is often misunderstood that lateral stability acts to roll the wings level, in response to bank angle. Unless there is sideslip, there are no laterally stabilising forces. Lateral stability only acts to reduce the sideslip angle, by rolling away from the sideslip.