The dressing of Aaron's sons in their priestly garments marks the climax of their sanctification. It is the final step before they begin the practical work of offering sacrifices in the Tabernacle [ביאור שטיינזלץ].
Moses brings the sons near to him, an action that might seem repetitive since they were already brought forward at the start of the ceremony. From a practical standpoint, the initial gathering was for their ritual immersion. Afterward, they waited on the sidelines while Moses focused on dressing and anointing Aaron. Once he finished with Aaron, Moses called the sons back to dress them [ביאור יש״ר]. This second gathering simply acknowledges the time that passed between these events [אבן עזרא]. Alternatively, bringing them near represents a spiritual elevation in holiness. Moses acts as a spiritual deputy, personally drawing them close and dressing them to elevate their sacred status [מלבי״ם, אדרת אליהו]. Another perspective suggests the sequence is a single continuous motion: the moment Moses brought them near, he immediately dressed them [אבן עזרא].
As Moses dresses them in tunics and sashes, pants are noticeably absent from the process. Out of modesty, Aaron's sons put the pants on themselves. Moses then dressed them in the remaining garments, the most significant being the tunic [פירושי רד צ הופמן, ברכת אשר על התורה].
Finally, Moses provides their head coverings, which were shaped differently than the turban worn by the High Priest [ביאור שטיינזלץ]. The action used to describe this step involves binding or tying [רש״י]. This reveals that the head covering was not a ready-made hat. Instead, it was a piece of fabric that Moses personally wrapped and tied around each of their heads [ברכת אשר על התורה]. The specific concept of binding implies something pressed firmly against the body, much like a bandage, indicating that the fabrics were wrapped very securely and tightly to their heads [ביאור יש״ר].