Let's start by understanding what "global market capitalization" means. On the NY Stock Exchange there are 3,066 companies listed. One of them is IBM. If you go to a site like this one, it tells you that IBM has 1,809,090,000 outstanding shares on October 21, 1999, and if you go to this page it tells you that the stock closed at $91 on October 21, 1999. That means that IBM's total capitalization is:
1,809,090,000 shares * $91 = $164,627,190,000
In other words, if all the shares of IBM were bought by someone today for $91 per share, the person would have to pay $164 billion to buy IBM. If you perform that calculation across all 3,066 companies on the NY Stock Exchange and add them all up, you get a total capitalization of $15 trillion.
The difference between the $6 trillion in the M3 money supply and the $15 trillion on the NYSE is that the $6 trillion are actual dollars, while the $15 trillion are all on paper. For example, on October 20, 1999, IBM closed at $107 per share, while on October 21, 1999 the number was $91 per share. The stock's price fell $16 in one day. 69,444,800 shares traded hands during the day of October 21 (about 3.8% of the total available shares). In terms of capitalization, IBM's shares lost:
1,809,090,000 shares * $16 = $28,945,440,000
On paper, $28 billion evaporated in one day. However, the vast majority of shares (96.2%) did not trade hands. All of those shareholders who did not trade their shares lost money only on paper, not in reality. If the stock bounces back to $107 tomorrow, then on paper they've lost nothing at all.
What this shows is that there is a difference between cash and value. There is a limited amount of cash, but there are many different things that have value to people -- cars, boats, houses, buildings, gold, land, books, roads, stocks and so on. These things all have value. In order to transfer ownership, we use cash to represent the value. Cash is the universal representation of value. If we didn't have cash, we would have to exchange objects of equal value whenever we wanted to buy something. That's called bartering, and it's generally inconvenient. As a society we agree to use the limited quantity of cash as a universal object of value in our transactions because it makes transactions a lot easier.
For more information on stocks and the stock market, see How Stocks Work.