The description of Ignatius' head contributes to the narrator's presentation that Ignatius looks unpleasant.
Explanation:
Ignatius is a very peculiar man and he causes people to be strange, because of the way he dresses, how he acts, his behavior and even his appearance, which is neither pleasant nor admirable. To reinforce the impression that Ignatius' appearance is bad, the author inserts the information that his head looked like a "fleshy balloon", which shows that he was ugly and that this contributed to people seeing him negative.
Notice how the word soliloquy is a bit like the word 'solo'. This is basically what it is: a solo in drama, where somebody is projecting their inner thoughts. This gives the audience direct access to the character's feelings.
