An unrealized loss occurs when a stock decreases after an investor buys it, but he or she has yet to sell it. If a large loss remains unrealized, the investor is probably hoping the stock's fortunes will turn around and the stock's worth will increase past the price at which it was purchased. If the stock rose back above the original price, then the investor would have an unrealized gain for the time he or she still holds onto the stock.
For example, say you buy shares in TSJ Sports Conglomerate at $10 per share, and then shortly afterwards the stock's price plummets to $3 per share, but you do not sell. At this point, you have an unrealized loss on this stock of $7 per share, because the value of your position is $7 dollars less than when you first entered into the position. Let's say the company's fortunes then shift and the share price soars to $18. Since you have still not sold the stock, you'd now have an unrealized gain of $8 per share ($8 above where you first bought in).
Gains or losses are said to be "realized" when a stock is sold. This is especially important from a tax perspective as, in general, capital gains are taxed only when they are realized. Unrealized gains and losses are also commonly known as "paper" profits or losses, which implies that the gain/loss is only real "on paper." This may be true from a tax perspective, but remember that a loss is a loss, whether it's been realized or not.
In addition to the extremely helpful video from Investopedia, keep in mind:
Whenever an asset is exchanged or sold, the IRS considers that event "realization". Usually whenever realization occurs, "recognition" (the inclusion into taxable income) must occur unless there is an exemption. As long as assets aren't exchanged or sold there is no realization therefore the term "unrealized".
Example: You buy XYZ stock for $1 on Jan 1st and on July 22nd it is worth $10. You have an "unrealized" gain of $9.
Hope this helps!