Abraham Simpson is the son of Mabel Simpson and Virgil Simpson. Abraham was presumably named after Abraham Lincoln who directly helped Virgil and Mabel escape from pursuing slaveholders. Abraham is also the great-grandfather of Abraham "Grampa" Simpson and presumably his namesake.
According to Grampa, his great-grandfather (possiby Abraham I) was trying to find a cheap substitute for holy water and instead invented what would become Simpson & Son Revitalizing Tonic.
When Mabel and Virgil got married, they had a son and named him after the president at the time, Abraham Lincoln. He is only seen in brief moment wearing Lincoln's hat he gave to them. He strongly resembles Bart Simpson, but with ruffled hair.