It is and was a custom among Arabs that if a person possessed a characteristic, he may be called the father of that trait. For example, Abu Jahl was not called that because he had a son named Jahl, even though Abu Jahl literally means the Father of Jahl. Jahl means ignorance. But neither did this mean that his son was ignorant. Rather, this epithet was applied to him because he was said to personify ignorance so much so that he could be considered the father of that trait - the father of ignorance.
If Imam Hussain (as) had not sacrificed as he did on the plains of Kerbala, then today Allah swt would not be worshipped as He should be because the purity of Islam would have lost to the corrupted forms of Islam favored by the killers of Imam Hussein (as). As a result, none of us today would be worthy of the title Abdullah, or servant/slave of Allah swt. Thus Hussein (as) could be said to have given his life for the protection of the existence of Abdullahs today. Any person who is able to submit to Allah swt has this blessing through the sacrifice of Imam (as), hence he has the title of the "father of the worshipper of Allah."
- paraphrased from A Short Commentary of Ziyarat Ashura available on al-islam.org.