Out of all the sensations and preoccupations that engage us through the day, we tend to prioritize based on the importance of certain things. Getting to work on time is more important than eating a balanced breakfast, mulling over a paper one is writing for school is more important than being aware of one's surroundings. Zen doesn't change these priorities but it brings out of the woodwork the essential equality of everything we encounter. A mote of dust has as much claim to the dignity, if you will, of being part of reality as I do.
That doesn't mean that I stop what I'm doing for a mote of dust. But a Zen awareness changes the balance of value between foreground and background. Whatever I'm focused on is done at the same time with the awareness of the grandmotherly presence of all those little things looking lovingly over my shoulder. So cleaning is a way of showing respect for this greater set of presences that are always there with us in the background.