The 180 degree rule allows the audience to feel as though they are in the scene with the actors. Its a believable shot which also allows the audience to form a more personal relationship with either/both characters.
An example may be an action scene, such as a car chase, if a vehicle leaves the right side of the frame in one shot, it should enter from the left side of the frame in the next shot. Leaving from the right and entering from the right will create a similar sense of disorientation as in the dialogue example.
This is another example of the 180 degree rule, the dialogue between two actors, if the character in the orange shirt in the diagram is on the left and the character in the blue shirt is on the right, then orange shirt should be facing right at all times, even when the blue shirt is off the edge of the frame, and blue shirt should always be facing left. Shifting to the other side of the characters on a cut, so that blue is now on the right side and orange is on the left, will disorient the viewer, and break the flow of the scene.