A paper millionaire is a person who owns one million dollars or more in investments. The difference between a paper millionaire and an actual millionaire is that a paper millionaire has a significant portion of his money invested in stocks and other kinds of securities while an actual millionaire has most of his money either in savings or in investments that are not likely to drop in value. Stock market investments, however, can quickly rise and fall in value, which means that a person with lots of investments in the market can be a millionaire one day but not the next and vice versa.
Very often, when people have lots of money invested in the stock market, they will refer to their total worth as their worth "on paper." This means that, based on reports of the performance of their stocks, they are worth a certain amount of money. This is where the term "paper millionaire" comes from. As reports change from day to day, so can one's status as a millionaire. As such, a paper millionaire does not have a firm grasp of the title of "millionaire."
When a certain market is growing very quickly, it is common for people invested in that market to become paper millionaires. A good example of this would be the dot-com bubble that burst in the early 2000s. There were lots of people invested in dot-com companies who had become paper millionaire only to fall below — far below, in some cases — a net worth of one million dollars.
For a paper millionaire to become an actual millionaire, his investments must be liquidated in part or in entirety from the stock market and put into a bank. For people who make their money with investments, this is not always an option. While some portion of investments in the stock market may be withdrawn as profits are earned, most investors keep part of their money in the stock market in hopes of making additional earnings in the future.
As it might take a while to siphon enough money out of stock market investments and into a bank account, it is possible for a person to be a paper millionaire for a long time before becoming an actual millionaire. This process can take even longer if the market is going through a rocky period or if the investor makes some investment choices that lead to a loss.