Assonance is when you have similar vowel sounds occurring in a number of words. So it is sort of like rhyming, except it does not generally come at the end of a word.
I think you can see examples of assonance right at the start of the Prologue. For example, Shakespeare writes
To me, the "o" sound in "holds" is the same as the one in "both." I also think that the "i" sound in "in" is the same as the second one in "dignity." So, to me, both of those are examples of assonance.
"Do with their death bury their parents' strife."
The "air" sound in their and parent's is an example of an assonance.