Alliteration is the defining feature of poetry in Anglo-Saxon. Just as in the modern day our first thought about what makes a poem will probably be that it will rhyme—although this is not always the case—in the Anglo-Saxon period, poetry was defined by the use of alliteration to unite two half-lines, which are usually represented with a break or gap in between. Many translations of Anglo-Saxon literature attempt to preserve this alliteration, but translations have different purposes. Some seek to be especially true to the meaning, rather than the form, of the verse and will therefore not preserve the alliteration. For this reason, it is always preferable to read Beowulf and other Anglo-Saxon texts in the original language with a page translation if you need one. If you look at the poem in Anglo-Saxon, you will see this alliteration is continually present throughout the poem. Here is an example in the opening two lines:
Hwaet! We Gardena in geardagum
þéodcyninga þrym gefrúnon
In modern English, this does not alliterate. It is something like, "So! We, the Spear-Danes, in the olden days, / heard tell of the glory of the clan kings." But in Anglo-Saxon, the alliteration is an essential part of the poetic form.
Look at the poem in Anglo-Saxon in the link below, and you will see that this continues throughout the poem.