光 (light) on the left supplies the core meaning: brightness and dazzling brilliance. 耀 is one of the few common characters where the explicit light element is preserved on the surface, making the glow-and-shine sense unmistakable. Indexed under Kangxi #124 羽 (yǔ) by tradition, taken from the iridescent feathers buried inside 翟 on the right.
翟 (dí, a pheasant with iridescent plumage) supplies the sound, drifted to yào. The bird's shimmering feathers add a flavour of dazzle that fits perfectly. The same phonetic also drives 跃 yuè (leap) and 濯 zhuó (wash bright).
Filed under radical 羽 (yǔ, #124) by convention. 羽 is not a separate component in 耀, so no strokes are highlighted.
