Nephilim is the name of the forbidden legacy of a Demon-Angel Hybrid. There have been no Nephilim in existance but they are foretold to have the Ultimate abilities of both Angel and Demon. Dante and Vergil were once considered to be Nephilim but are not due to their human heritage. Sparda is also not Nephilim due to the fact he casted away his Demon Genes to become an Angel.
Nephilim's are foretold to be the ultimate species, superior to even Angels and Demons. They are a forbidden mix and have the potential to be the greatest species to ever exist. They would posses the abilities of both Angel and Demon, able to cross over between each realm with ease.