Note: this writeup ins one of a series attempting a comprehensive overview of United States income taxation. All Code citations are to the Internal Revenue Code of 1986 as in effect on the date of the writing.
As noted in Section 61: Gross income defined, nearly every increase in wealth is income (subject to deductions, exceptions and exemptions) for purposes of the United States income tax. However, to be actually taxed, income must be realized. This does not necessarily mean "cashed out," but it is a related concept.
Essentially this means that if your Microsoft stock, for example, previously worth $10,000, is now, because the stock market is up, worth $20,000, you will not be taxed on the $10,000 of profit until you sell the stock or exchange it for something else (say, a fraction of a garage in Silicon Valley) which itself is worth $20,000. (Likewise, losses are not taxed until realized.) In other words, mere appreciation in value of an asset you continue to hold, while it is certainly in some way an accession to weath, will not be taxed until you get your hands on it in some other form. (There are a series of rules concerning tax-free exchanges with which this series will deal in due course.)
No individual tax advice is implied by any writeup in this series. Please consult your own tax advisor about any questions you may have about your personal situation.