EIFS needs to be cleaned for various reasons. Obviously, it can make it look better. Other reasons include preparing it for changing its color by painting it, and preparing it for applying a new basecoat and finish to it. Cleaning the wall before applying a new coating is critical in the last two cases. The reason is simply that the only thing holding the new materials onto the old finish is the bond between them. A clean surface is essential to achieving that bond. Remember that cleaning involves not just removing whatever is on the wall to start with but also whatever residue is left by the cleaning process itself.
The usual way to get plain dirt off EIFS is to scrub it with a bristle brush using warm water and mild soap. EIFS finishes are water-based, and when they become wet in the normal course of their existence as a wall material, they become slightly softer. In this softer condition, tiny particles can get lodged into the finish. When the finish dries again, these particles become part of the finish. These particles sometimes simply do not come off. More aggressive cleaning methods are needed.