1. The thousand-year period (or decade) starting in the year 2010.
2. An second chance for those who missed the real millennium celebrations because they believed the Y2K disaster hype and spent New Year's Eve 2000 locked in a concrete bunker anticipating the end of the world (which is now slated for 2012).
3. A more impressive-sounding name for a 10th anniversary, an alternate word for decade, which is too similar to "decayed" and "decadence" to sound as positive.
"This New Year's I'll be partying like it's 2009 cuz it's the start of the new miltennium!"
"Since there's no Y2K10 bug, we can ring in the miltennium by celebrating instead of worrying like at the millennium."
Urban Dictionary has been around for a whole miltennium!