Gains and losses are only "real" when shares are sold or withdrawals are made, but up until that point the gains were more of a notional amount, and are said to be "unrealized."
A more salient way to understand unrealized gains is to look at the opposite: unrealized losses. If a person makes an investment of $1,000 and the value of the shares drops sharply the next week, has the person lost any money? The answer of course is no, not unless he sells the shares and takes the lower market price for them.
If the person does not sell the shares while they are valued lower, and their values go back up after that, he has avoided realizing losses and may be able to realize gains in the future.
Unrealized gains might be disacussed with regards to taxes: if a stock is held for years and is valued significantly higher than when it was purchased, no taxes will be due year to year (except in the case of dividend distributions) on the unrealized gains, but the minute the amounts over the purchaser's cost basis are liquidated for cash settlement, the purchaser will have to report those gains for tax purposes since a gain has been realized.
What is Form 6781: Gains and Losses from Section 125 Contracts and Straddles?
What are the Tax Implications for Making a Profit (or Loss) On a Stock?