what does the use of alliteration add to the work?
The Anglo-Saxons used many literary devices, but chief among them are alliteration, caesura, and kennings. All three are used as memory devices since the story tellers had thousands of stories to tell from memory (no written language among the common folk) in keeping with the oral tradition of the times. It is much like rap music today...rhythm, rhyme, and a certain set of phrases to be pulled upon when needed to fit a particular meter.
Alliteration: repetition of consonant sounds at the beginnings of words "The mighty water witch whirled toward him"
Kenning: a phrase which renames the thing about which it refers "whale road" for the sea "ring-giver" for king
Caesura: a break in the line of poetry usually indicated by a comman where there are equal syllables on either side of the break. Sometimes even alliteration takes place on either side of the comma.
Alliteration in Beowulf typically adds to the physically sensory perception. If there is a battle, the "B" sound is emphasized, ie, when Grendel attacks, "B's" are prominent, "Great bodies beating at its beautiful walls." For a lovely side-by-side analysis of the original language and the English translation, see the translation by Robert Fagels, who faithfully renders the Old English into a modern text.