A bastard - Probably, a child born of incest or adultery.
Even to his tenth generation - i. e. (see the next verse and Nehemiah 13:1), forever. Ten is the number of perfection and completeness.
Related Commentaries of Deuteronomy 23:2
Deuteronomy 23:2
2 A bastard shall not enter into the congregation of the LORD; even to his tenth generation shall he not enter into the congregation of the LORD.