Because Beowulf is essentially a Christian poem despite its mixture of Christian and pagan elements, the first mention of Grendel, which would certainly have been fearsome to the poem's listeners:
That fiend from Hell . . .was called Grendel,/notorious bush-roamer, at home on the moors. . . since the Shaper [that is, God] had condemned him/as Cain's kinsman. (ll. 102-106)
The poet, in order to place Grendel in the Christian world and make his outcast status understood, must describe him as the descendant of Cain, who killed his own brother, Abel, and was cast out of Adam's family by God. Grendel, therefore, falls into the category of an unnatural killer and enemy of mankind.
Shortly after his introduction into the poem, we see Grendel attacking the Danes in Heorot, described in even more horrific terms:
The sinful creature,/grim and greedy . . . savage and spiteful, and seized at least thirty thanes; thence he went back,/ exulting in plunder, to tramp home. . . . (ll. 120-124)
This scene depicts Grendel's first attack on Heorot, and immediately following this description, the poet makes it clear that Grendel "committed worse murders, and with no remorse for/his killings and crimes; he was too caught up in them." (ll. 135-137). What makes Grendel so fearsome to the Danes is not just the attacks but that Grendel attacks without remorse and without stopping until he has killed every Dane who tries to sleep in Heorot. The phrase "he was too caught up in them" suggests that Grendel's attacks can never stop because Grendel doesn't have the ability to stop himself.
Perhaps the most horrific description of Grendel occurs when Beowulf and his Geats are in Heorot, and Grendel begins his attack:
. . . he suddenly seized/and slashed up a sleeping warrior,/crunched his bonecage, drank the blood from his veins/and swallowed great morsels; soon he had gobbled down the lifeless man. . . . (ll. 741-744)
It is one thing to be killed in a battle with Grendel, but it's quite another thing to become Grendel's meal during a battle. On a scale of ways to die, being eaten alive is probably the most horrific manner of death. The fearsomeness of this encounter would have been enhanced when the listeners recall that Grendel, who is committing an unspeakable act, was once part of God's family. His cannibalism, of course, places him far outside the pale of mankind.
Grendel's defeat at Beowulf's hands, of course, is well deserved and, in a Christian context, part of God's just revenge upon Grendel. But Grendel's fearsome attacks on mankind--implacable, hateful, unnatural--would have reminded Beowulf's audience that their lives could conceivably be ended by equally fearsome beings who stalked the outskirts of their Christian world.