An unrealized gain is a profit made on a stock that has not yet been sold. It is also referred to as paper gains or paper money. Although the gain exists and the investor who owns the stock could sell at any time, the gain is not realized or claimed until the investor sells the stock and takes his profits.
Stocks are partial ownership shares in public companies. A stock can be bought and sold on the stock exchange through stock brokers and discount online brokers. Stocks go up and down based on how much each investor is willing to pay for them. The bid, which refers to what people will pay, and the ask, which refers to what people are asking, can change on a second-by-second basis when the stock exchange is open.
An investor who buys a stock can buy as many shares as he can afford. When each share goes up in value, he makes money on that particular share of the stock. If he has multiple shares, he makes a profit on each share he owns. For example, if an investor owns 100 shares of a stock that goes up $0.10 US Dollars (USD) he makes 100 x $0.10 USD or $10 USD.
Any money the investor makes when a stock goes up is considered unrealized gain until the investor sells the stock. The gain is referred to as unrealized gain because the stock could go back down in price and the investor could lose the money he made. Thus, until the investor sells the stock and actually takes the profit he earned, he hasn't really made money or gained anything on the stock itself.
When an investor sells a stock, the gain is no longer an unrealized gain. At that point, the investor is taxed on the profits he makes on the given stock. If he owned the stock for a long period of time — more than one year — he must pay capital gains taxes within the United States tax code. If he owned the stock for less than one year, the realized gains are taxed as ordinary income.
Many investors are referred to as having paper wealth, or even as being paper millionaires, because of the unrealized gain on stocks they own. If the stocks are not sold and the market drops dramatically, these millions of dollars in gains essentially disappear. This occurred when the stock market crashed in 2000, in an event widely considered the "burst" of the tech bubble.