Amina Inloes, Amina Inloes is originally from the US and has a PhD in Islamic Studies from the University of Exeter on Shi'a hadith. She is the program leader for the MA Islamic Studies program at the... Answered 3 years ago

It means "the father of Abdullah". Arabs traditionally addressed men by the name of their firstborn son rather than by their first names. This was considered a respectful way to address someone. (This is also common today.) So when Imam Husain is referred to as "Aba Abdillah" it is a conventional usage of his time. Other men who had a son called Abdullah are also called "Aba Abdillah", and it is not something specific to or limited to Imam Husain. (Occasionally, some people think this and are shocked to hear "Aba Abdillah" used for anyone else.)

("Abdillah" instead of "Abdullah" is used due to the grammatical construction used when addressing someone, since Arabic words are adjusted slightly when they are used in different ways grammatically)