Utilities of a cape
When faced with environmental dangers like dark rain, it isn't always obvious whether one's eminent or inner light is being drained. Eminent light is almost always drained first, but the issue is discerning when the environment starts to drain one's inner light. This is the first function of a cape. The glyphs commonly seen on the back of capes react to the glow of one's light, and the brighter one's eminent light is, the more glyphs will glow in response. If all the glyphs are dark, that's a good sign that one's inner light is in danger.
Among spell casters, the number of glyphs on one's cape also serve as an approximate indicator of power level. The more glyphs on their cape, the more advanced their abilities probably are.
Capes with this function may not be accurate if it's brand new or if the cape doesn't belong to you. This is because capes need some time to acclimate to one's light levels. Initial discrepancies can be especially egregious when people of different light levels swap capes. For example, if Mufotsuki, someone with a higher level, swapped capes with Piripu, someone with a lower light level, both of their capes would give incorrect readings. Piripu's cape, while on Mufotsuki's back, may indicate that her light's brightness is at 100% even though it's really at 80%. Likewise, Mufotsuki's cape, while on Piripu's back, may say his light's brightness is at 80%, even though it's really at 100%.
The other, more well-known, function of a cape is as a tool for flight. One can fly with a partial cape or no cape at all, but the feeling can be clumsy to the inexperienced. Having a cape serve as one's wings offers more control and makes the experience feel more natural.
Capes also serve as a fashion statement, but everyone knows that.