Assonance is the repetition of vowel sounds to create internal rhyming within phrases or sentences, and together with alliteration and consonance serves as one of the building blocks of verse.Assonance does not have to be a rhyme; the identity of which depends merely on sequence of both vowel and consonant sounds.ssonance is the repetition of vowel sounds to create internal rhyming within phrases or sentences, and together with alliteration and consonance serves as one of the building blocks of verse.