و على آله
“…and on his family”
Imam Taftazani says that the original form of آل is أهل because the diminutive form (تصغير) of both is أهيل, which shows the base letters as أ-ه-ل.
As both ه and ء originate from the same place, the ه is replaced by ء. As the second ء is sakin, we drop that one and prolong the first one.
The diminutive form or the broken plural shows the base letters of a word, e.g. دنانير is the plural of dinar (دينار). The broken plural has 2 “noons” (ن) but the singular has only one, so the broken plural shows that one of the “noons” from the base letters has been dropped in the singular.
أهل is used to refer to the family of normal people whereas آل is used exclusively for people of nobility and influence. This nobility can be nobility in the hereafter, or even just in this world, e.g. the Qur’an says:
فَالْتَقَطَهُ ءَالُ فِرْعَوْنَ
“Then the household of Fir`awn picked him up…” [al-Qasas:8]