Not all films need to be explained rationally or have a logical-rational plot.
Some films, like this one, should simply be seen and experienced with empathy trying to understand the message, the fundamental feeling the director wants to convey to us.
Besides it is often difficult to distinguish "real" scenes from those simply experienced in the mind of the narrator (are these the scenes that end with a red fade?).
What is remarkable is the way the word, the tale, manages to transform (the perception) of reality, and in fact Umberto - the main character of the film - calls himself "one who tells lies (or fables) for a living."
A story, a plot, a tale does not have to be functional but simply "is it good or is it bad" - says the film's protagonist - and so not only the story becomes important but also the way it is told
The whole film can be considered an ideal, imaginary construction:
for example in the plot there are no legal "hassles" of his separated wife over child support, the black waiter with the white beard looks as if he came straight out of Aladdin's Lamp (so wise, sensitive, and thoughtful is he), Rome is a beautiful, silent city almost devoid of people and hustle and bustle, the place where he meets an old girlfriend is unrealistically silent, and so on.
Unlike the protagonist of the film many people and many young people nowadays fill their lives with many actions and concrete facts; however they are not fully aware of what they do and hence the sense of emptiness that they often perceive in their existences.