First hit on Google. "An individual who has achieved a high net worth as a result of the large total market value of the assets he or she owns. This phenomenon usually occurs when investors buy marketable securities that are later bid up to much higher prices on the open market. While this creates large amounts of "paper profit", the paper millionaire's riches usually aren't safe until these holdings are liquidated."
Even better examples than the employees at Twitter are startup founders. They start a company and quickly raise 500k at a 2M pre money valuation. Suddenly, they own $1M of a $2.5M company. A millionaire, at least on paper. Not much changes in their lifestyle though. They still can't make a down payment on a house and generally don't drive nice cars. And that's the point of the title "paper millionaire". It doesn't mean much if you can't do anything with it.
The term "paper millionaire" means exactly as it sounds - someone who is a millionaire, but strictly on paper.
Most of the shares these Twitter employees have received cannot be sold until a certain amount of time. So the money is "on paper". They don't millions of dollars in their bank accounts - rather, they simply owns shares that are worth a million dollars.
I think liquidity is a key distinction. Many of those Twitter employees are in a lockdown(?) period post IPO where they are not allowed to sell their shares (typically 6 months). Thus they don't have the option of becoming cash millionaires right now. (Many startup founders are this way post series A)
Compare this to a case where someone owns $1MM worth of Google shares, purchased on the open market. Even though they don't have cash, it's basically as if they own cash, since you can liquidate the shares right away.
