Assonance is the repetition of a vowel sound within a line of poetry. An example of assonance is "the rash wants to dash away from my cash." While this does not necessarily make sense, the repetition of the "a" sound within rash, dash, and cash is obvious.
As for an example of assonance taken from Charles W. Kenneddy's translation of Beowulf, assonance is found in line 41.
To a mighty host'. Then his mind was moved.
In this line, the "i" sound in both mighty and mind denote assonance.
Another example of assonance is found in line 53.
The Hall of the Hart; and the king kept well.
Here, the "a" sound in hall and hart repeat. Again, this repetition of the vowel sound exemplifies assonance.