What this means is that most of the "money supply" is not in the form of cash.
There are three levels of money supply, right? There is M1, M2 and M3 with M1 being the most liquid and M3 being the least. Only about half of M1 is in cash in the US and none of M2 and M3 are in cash.
So most of the money in the United States only exists in the records of banks and other institutions.
But this is not new. All that's new is that the money is now in computer files when before it used to be written down on ledger books or whatever banks used to use to keep their records.
Money is the medium for exchange of goods or services. Without money people will have to barter the goods and services they have or produce in exchange for other goods and services they want. This process of exchange becomes very easy when people are able to exchange goods and services for money. Thus money acts as lubricant that facilitates the process of exchange in an economy.
We generally think of money as coins and paper currency. But in reality the money that is represented by assets like money in bank accounts is also are used for payments, and therefore is money. For example, we may make payment by cheque. This type of money including coins, currency and deposits in bank checking or current accounts is designated as M1 type of money. There is another broader concept of money called M2 money. This type of money includes all M1 type of money plus certain other type of liquid assets such as saving accounts, and money market funds.
The statement that "most of the money supply is made of intangible computer entries" is pointing towards the fact that in the total amount of M2 money supply, the proportion of the physical money in form of coins and currency notes is very small. Most of M2 money is in form of other liquid assets, and amount of this kind of money is not represented by any physical asset but by entries in accounts of various organizations.