The computer models that are used today are incredibly complex, as they try to reduce the complicated physics that govern atmospheric processes to a set of equations that can be worked forward in time to generate a prediction. In order for these equations to be solvable by the most powerful computers in the world, some assumptions (or compromises) need to be made. Many of these involve ignoring some very small-scale processes in order to keep the equations manageable as far as the numeric processes of solving them are concerned.
Sometimes the mathematical representations of these small-scale processes can cause the equations to become unstable and thus yield unrealistic solutions. The problem is that the small-scale processes do exist in the atmosphere and while often they do not have a dramatic impact on the larger-scale weather patterns, there are situations where they can have a significant effect. The trick to getting the best accuracy is to find out when they will be more important and to include them at that time. The verification procedure allows researchers to test various ways of setting up the computer models to see what will provide the best result.
Another facet of the computer models that is difficult to represent mathematically is the actual surface of the earth. Because the nature of the surface is different from place to place (ocean versus land, rough terrain versus smoother ground, etc.) and also from time to time (snow- and ice-covered at certain times and not at other times, for example) the amount of friction between the air and the surface will vary, and this needs to be factored into the models. The differing elevation of the land also has a significant impact on how the atmosphere behaves around mountain ranges and where the land meets the ocean.
Here, once again, the verification procedure can identify certain geographic areas where the models may not perform as well as they should, which can then drive further improvements moving forward.