According to Wikipedia, the word "mambo" has at least two meanings:
In the Voodoo religion in Haiti, it refers to the female high priest, "whose responsibility it is to preserve the rituals and songs and maintain the relationship between the spirits and the community as a whole (though some of this is the responsibility of the whole community as well). They are entrusted with leading the service of all of the spirits of their lineage."
As a "music form and dance style", "the word derives from a ki-kongo based language, the language spoken by West-Central African slaves taken to Cuba". It means "conversation with the gods".
Whichever one Hou was thinking when he titled his Millennium Mambo, he was trying to make a film about modern life where the main purpose was to have an interaction with the invisible spirituality beyond the visible world (through the character of Vicky, if we accept the first definition).
Actually, again according to Wikipedia, the word is also a greeting in Swahili 'commonly used by young people in East African countries especially Tanzania and some parts of Kenya. It's considered a slang greeting, and translates to "things?" as in "how are things?"'. Is this Hou saying "Hello!" to the new millennium and asking, somehow ironically, "how are things"?
All of these work as explanations... I'm sure there could be others.
Bland lives, lived without hopes, without love... Lives spent smoking cigarettes, perhaps because dying isn't necessarily worse than living... Meaningless music all around...
Millennium Mambo is a film of despair. The only character who seems to have real hopes about life is a 80 year old grandma living in a village far from the urban landscape. Not so surprisingly within the context, and considering Hou's love for cinema, this same village also has a film festival.
It is a film of despair, a continuation of his previous film The Flowers of Shanghai (1998) in lots of ways, just in a different time period. I'd like to point out that the films that will follow Millennium Mambo will all have very joyful, happy, hopeful, and loveful moments, just as there are in earlier movies, beginning from The Green, Green Grass of Home (1983). There are many films of his I haven't seen but I guess it wouldn't be a mistake to call this period a relatively depressed point in his filmography.
The moments of joy in Mambo are all too brief to give us hope, they look almost as a revolt to the blandness all around. In a film like The Flight of the Red Balloon, six years later, there is real faith in human warmth and the power of love.
You can find here Andrew Schenker's wonderful blog post about the sound on Hou's Millenium Mambo.