Well this is the question, isn't it? Especially when you think of the scenes like the introduction of random "commoners" and "men without occupation" in front of Buckingham Palace. They are brought to our attention by the journey of one of Woolf's fluid setting mechanisms: the journey of the imposing black car.
Woolf is writing in stream of consciousness that gives her access to her characters' thoughts, motives and feelings. Stream of consciousness flows in and out of thoughts in seemingly random shifts (it is important to note the randomness is only seeming because each shift and stream has been carefully orchestrated by Woolf to precisely achieve some deliberate end and some deliberate perception and to deliberately fulfill some function in narrative construction). We might think of the use of the many characters as analogous to (an analogy to) stream of consciousness: Woolf sets up a stream of characters that flows in and out of the feelings, thoughts and motives of collective society.
Perhaps the importance lies in her attempt to see all humanity as joined as one in one Jungian universal, archetypal consciousness: whatever happens here to Septimus happens there to the "poor people all of them" in front of Buckingham Palace with flag waving and happens to the Queen who is at home. This universal shared experience, Woolf may be suggesting, is proven by the path of the "aeroplane" and journey of the ominous black car of the Royal household. The presence of the objects unites all the people nearby, all "Passers-by."
The journeys of these objects (e.g., car, aeroplane) continue to unite more and more, drawing person after person into the comet's tail of one shared experience. This unifying drawing-in is a metaphor for the drawn-in unified bound-in experience of universal consciousness. Woolf seems to be saying something like:
- "Have you doubts that we are all part of one conscious mind, that we all share one common experience? You have but to look up; you have but to look out the window (of your soul, of your heart, of your mind, of your Self) to see that all is shared, all is one. If a Royal car backfires, we all experience it. If Septimus wishes to die, we all experience it--even--even if we cannot sort out the details, even if we cannot recognize the personages, even if we don't know the facts behind the required action, we experience all together. None know who was in the car behind the "square of dove grey"; none know who Septimus is nor that he wishes his death nor why he wishes it (Whose language is it he does not yet know?), but all is experienced by all. All are united under the same events in the same sky, under the same mind in the universal consciousness."
An important point to keep in mind is that one of Woolf's professed purposes is to create a woman's style that expresses women's way of thinking and perceiving. She professedly aims to separate herself from the literary and thought style of generations of male writers--traced all the way back to Greek and Roman predecessors--who, in her view, have imposed a mode of thought and writing that is said to be universal but, she asserts, is in fact only universal to the male mind.
In more practical terms of importance (Would Woolf separate "practical" from "seeming" and from "actual?" Perhaps not.) ... in more practical terms, the many characters often perform functions that advance the theme or character development. For instance, Scrope Purvis advances Clarissa's character development by letting us know her appearance, how others perceive her ("a touch of the bird about her") and how her recent illness has effected her ("grown very white"). In another instance, the random poor people in front of the Palace, who direct our attention to the aeroplane, rather directly bring up the thematic concern of class suffering: "Little Mr. Bowley ... tut-tut — actually had tears in his eyes." While there are far too many instances to analyze in eNotes, these two directions (psychological and literary function) will help you in your own analysis of other minor characters in Mrs. Dalloway.