The Danes were a warlike people who feared very little. But what they did fear and even respect was strength and cunning, as do most warrior races. They spent their days preparing for conquest and being the best at what they did. Anyone or anything that they could not defeat with brute force was a threat to their very existence.
Such an enemy was epitomized in Grendel. His very existence, they believed, was a result of the curse on Cain when he was driven from the presence of God and God's servants after the terrible sin of slaying his own brother.
Just as Cain was an outcast in the world, so is Grendel. He is the very essence of evil. He wanders, he attacks, he cannibalizes humans, he destroys, he haunts, he is seemingly undefeatable. In a nutshell, he is everything the Danes fear.