Mudaf ilayh: the completing part
مُضَاف إِلَيْهِmudaf ilayh - completing part of idafah
Mudaf ilayh is the second part of an idafah possessive phrase in Arabic grammar.
Simple explanation
مُضَاف إِلَيْهِ (mudaf ilayh) is the second part of an idafah.
It completes the relationship started by the mudaf.