In the formal sense of the word, I came to understand it as the generation that reached adulthood sometime during the 2000's.
So like someone born between 1982 and 1991 or something. However, that's considered a somewhat conservative analysis of the generation; some people have extended the end range and use it to describe people reaching adulthood at some point during the early-mid 2010's as well. All in all, it's a nebulous term used to describe the current youth generation, a la Greatest Generation, Baby Boomer, GenX, all that BS.
In the negative, straw-man, ageist slur sense of the word, it's used to describe a young person (teens/tweens) who's spoiled, acts entitled and thinks the world owes him a living because CAPITALISM IS GREED; he supports a strong welfare state, stays at home often and plays video games or some **** while taking advantage of welfare income, thinks jobs are only for healthcare, and complains about how the world is unfair because he's expected to spend at least 40 hours a week working and competing with others to earn a living, and everyone's sick of him comparing the United States to some social democracy in north Europe and be all LOOK LOOK SEE SEE SOCIALISM WORKS WHY CAN'T WE HAVE THAT UNIVERSAL BASIC INCOME FTW. They also speak in stupid internet terms in real-life, won't put their smartphones away, and seem to have their entire lives revolve around Facebook, Twitter, Tumblr, and other "social" media that seems to substitute for putting their technology down for at least five minutes and actually talk to a real person. You know, back in mah day, before America got ruined by the welfare liberals and hippies, we had to actually dial the telephone to talk to someone over long distances and hear their voices but often we'd go outside and open the white-picket fence and say "howdy, neighbor" to our next door nuclear family in our neighborhood with no black people like it should've stayed and VHS was the best thang, ya fink! Now git off mah lawn. Vote Trump: he's going to make America great again and build a wall to keep the spanish mongolians out and if you're lucky, he'll make anime real!
The **** was I talking about? Oh, yeah, "millennials."
So, yeah.....a 20-something who acts lazy, spoiled, entitled, arrogant, whiny, excessively politically correct, acts enslaved by technology, and supports socialism. That's essentially what they're referring to. Most often it's used by Baby Boomers and Gen-X'ers who are sick of the young generation blaming them for the current state of the economy and wish they'd get up and either get a job or "do what [we] did when times were bad:" start their own business and create opportunities instead of waiting around for them to happen. [sic]
It's basically this generation's "Welfare Queen." It's a vague straw-man that people bring up to justify deregulation and welfare funding cuts. Or something that people use to blame for the problems of the modern world. Every generation has to put up with previous generations thinking they're the worst thing ever.