If people with money to invest had to go out and individually find a company whose bonds and shares they would buy, it would be difficult and risky to invest. From the entrepreneur's point of view, there would be no guarantee that they could get enough funding to start the business.
From the investors' point of view, they couldn't know if a company wouldn't just disappear and take their money with them.
And even if they spent quite a lot of effort establishing the company's credibility
The nature of moneyness can be better understood here.
Commercial banks are the best-known liquidity providers in the economy—though usually not by this title. Their business is better known as lending. They take an IOU, a promise to pay, and in return give a deposit—another promise to pay, just one that happens to be widely accepted as money.
As a result, the bank's assets are mostly other peoples' debt to the bank. Its liabilities, on the other side of the ledger, are mostly deposits. In earlier times, it was common for commercial banks to issue paper banknotes, but by now this is illegal in most countries.
There are a few other services as well. Pre-paid debit cards are a separate liability, for instance. This is in contrast to credit cards and cheques, which are not separate, instead "talking" to the deposits. When you pay with a credit card, the terminal immediately checks with the bank whether you have enough deposit, and if so, immediately transfers them. Obviously, a cheque only does this when it is deposited back to the bank. As a consequence, cheques can (and on occasion, have) circulated in the local economy for quite some time before being cleared at the bank.
Central banks are not inherently evil, but are very easy to be confused by. That's because they do several different things, and most people don't understand any of those. In my opinion, it would not only help understanding, but would be beneficial in the real world if these functions were separated.
When a person with deposits at one bank tries to pay a person with an account at a different bank, the first bank needs to pay the second. In some lucky cases, around the same time there is another transaction from the second bank to the first, thus settling the two banks' difference. But this cannot be relied on in practice.
Because there are many banks, if they had to settle transactions pairwise, the result would be a heap of ad hoc solutions. It is far better to have a single, central clearinghouse that every interbank transaction is routed through. The first bank pays the clearinghouse, which pays the second. At the end of the day, only net balances need to be moved to and from the clearing house. Furthermore, as each transaction from bank to bank results in exactly as much payment to the clearinghouse as from it, the sum of its balances does not change.
The key thing is to compare the balance sheet of a CB to a commercial bank. A normal bank owns mostly debt (bonds), and sometimes a little gold, foreign currencies, etc. And they owe money to their depositors, plus have some value (equity).
A CB owns mostly debt (bonds), some gold, etc. And they owe the cash circulating. Plus some equity.
This actually makes a lot of sense. If Something Bad™ happens, and the people all want to get rid of their money, the CB has to give them something. That is to say, the CB must own something to cover every single unit of currency that they have issued. This is the guarantee that the people won't one day wake up with worthless slips of paper in their wallet.
Of course, this isn't quite bulletproof. The debt that CBs own can go bust, as can other assets. But usually most of what they own is lots of bonds issued by the government of the country. And if those go bust, you usually have bigger problems on your hand.
Furthermore, they are the lender of last resort. This can be done even if all money is gold coins, and none can be printed. The point is that sometimes there's a "banking panic", and everyone wants to take their money out of the bank.
But as you remember, most of the bank's assets are personal and small-business IOUs, and the depositors will not accept those. If there is a run on a bank outside a banking panic, they can simply sell their debt assets to other banks, and pay the depositors with the money received. Or even more simply, ask for a short-term loan from the other banks.
During a panic, however, every bank is suffering from a run. Thus they aren't willing to buy debt from or make loans to each other. This can be seen in the bank-to-bank lending rate going through the roof.
Now, the lender of last resort can solve this problem. It keeps a much larger stock of money and other liquid assets on hand than normal banks. (With paper money, it can just print more, but that is not strictly necessary.) Thus they set a rate that is not normally competitive, at which they are willing to lend out their money to the banks.
When a panic hits, the banks simply take out such loans, and pay their depositors with it. Their assets are unchanged, while their liabilities to their depositors are replaced by a liability to the lender of last resort.
At the same time, the central bank starts to sell its liquid assets, and gets back about as much money as it has lent to the banks. Its liabilities don't change, while its liquid assets are replaced by the banks' promises to pay.
Lastly, as the people get their money from the banks, they use it to buy the assets of the central bank. Their liabilities are unchanged, their assets change from bank deposits to whatever the LoLR sold.
Of course, this works best if the central bank can just print more money, and simply buy short-term bonds of the banks. In this case, something slightly different happens: while the peoples' assets go from deposit to money, the central bank's balance sheet grows, as both liabilities (newly printed money) and assets (the banks promise to pay it back) are simultaneously added to it. However, as the previous paragraphs show, this is not necessary, and the lender of last resort function can work without issuing new money.
After the panic subsides, the banks pay back the central bank's loans while the people once more put their money in their deposits.
And if all that wasn't enough, central banks are also the monetary authority. This means they decide how the unit of account moves.
Now, to be rather theoretical, all banks are monetary authorities of their own. After all, it is quite possible for a deposit or banknote issued by one bank to have different value than those of another. This mostly happens when the issuing bank fails.
In practice, we do not think about this much, because all banks maintain a fixed conversion rate to the central bank's money, and they admit unlimited conversion in each direction. That is to say, they act as currency boards.
Some central banks also act as currency boards. For example, the Bulgarian Lev has been pegged at 1:1 to the Deutsche Mark (and since then, the euro at the DM-€ conversion rate) for over two decades. Historically, countries in the Bretton Woods agreement have pegged to the dollar.
Today several countries peg to the dollar, and some peg to currency baskets. The latter means that for every unit of their own currency, they give e.g. 0.5 USD and 0.5 EUR. In earlier times, some central banks (and even independent banks) have acted as currency boards to gold. If someone brought in a fixed amount of gold, they received a unit of currency, and vice versa. A famous example of this, 20.63 dollars could be converted into one ounce of gold and back in any bank in the US.
Perhaps unfortunately, nowadays the most important central banks consider it beneath them to peg to anything else. This is largely due to the widespread attitude that the Great Depression was caused by some sort of deflation, rather than by raised tariffs and taxation. As a result, they try to target some specified rate of change in the CPI or NGDP, even though in fixed-exchange-rate times it would have been perfectly obvious that doing so is nonsense. During the Bretton Woods era (and even before that, with independent pegs to gold), various countries had very different NGDP and CPI growth rates.
Mutual funds are, in some way, a funhouse mirror image of banks. They collect a wide variety of small IOUs, shares and other kinds of assets, and issue shares. This has a number of important consequences.
Firstly, there is no such thing as a bank run. Because the price of the shares inherently floats, there is no peg to be broken. In a bank's case, it promised that each deposit or note will be redeemed at a given price. If the bank lacks the assets with which to honor the promise, the peg will break sooner or later. But until the peg is officially given up, depositors will "run the bank" to redeem their deposits at par, above net asset value and thus market price.
Secondly, the mutual fund cannot go bankrupt. Even if its assets lose a massive fraction of their value, because its liabilities are entirely in equity, it doesn't go bankrupt. The price of its shares falls a lot, perhaps, but it doesn't go bankrupt.
Thirdly, under the names of credit union, mutual savings bank or cooperative bank, these funds are perfectly capable of making loans. Indeed, they are able to make loans in two different ways (not that banks couldn't). If the fund has enough money, it can simply purchase the bond that the borrower is effectively offering. This form of lending doesn't affect the liabilities side of the balance sheet.
Alternatively, the fund can do what banks do, and issue a new liability at the same time as it acquires the new asset. In this case, this would be a share of the fund, that could be sold on. Interestingly, if the shares of the fund have a large secondary market, they will be more valuable than the personal IOU. If the fund wants to do a fair deal with the borrower, rather than giving away this bonus for free, then the shares of the other members will appreciate slightly.