(1) rare. Is 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. For example, in the phrase “Do you like blue?”, the “oo” (ou/ue) sound is repeated within the sentence and is assonant. Source Wikipedia
(2) common. The sound of someone repeating technical information to another person that they don’t really understand. Typically as if they knew what they were talking about and usually just after you have imparted the information to the first person. Emphasis on ‘ass’.
The core network has just failed for an unknown purpose, you furiously hopping form router to router looking for cause, and you have some ideas. The Manager comes over and asks “What is the problem, do we know yet ?”, since that will obviously help you fix the problem.
So you stop, rummage around in your mind for a simple, ‘less than two syllable’ response knowing that you are wasting valuable time, and spurt it out.
Then the Senior Manager arrives, and asks, you guessed it, “What’s the problem ?”. The Manager then responds with some approximate of the gibberish you just told him.
Now that is Assonance.
Note: even though you are sitting less than two meters and could easily answer yourself, you are never consulted.