(you can find this post also on my website - http://217.61.121.241/2018/01/02/bank_definition/)

In my opinion, there seem to be three central functions of a bank, of which each is fairly different.

1. The first function, which seems most obvious, is that banks are well-known and trustworthy institutions which people are happy to deposit their
   money in, whilst the companies which a bank lends to aren't necessarily as well-known or trustworthy (at least to most people).
2. The second function, is that banks maturity-transform assets. They make loans
   which may be paid off over a long period of time, such as 30 years. Yet the deposits the banks owe are short-term, often callable on demand! This
   property is what causes the feared bankrun, in which scared depositers suddenly withdraw all their money at once. This is called maturity
   transformation because the banks assets are long-term whilst the bank liabilities (deposits) are short-term.
3. The third function, is that banks
   offer an easy way of transferring your assets - it's a long and lengthy process to transfer a share, bond or block of gold to someone, whilst a bank
   transfer these days is instant and feeless.

The problem here is that many instuitions have some of these functions but not all of them. For example, PayPal let's you transfer cash, so comes
under the third function. A mutual fund or private equity firm arguably comes under the first function, and maybe even under the third, but doesn't
come under the second. We might also even have a bank-like entity which does 2, and 3, but not 1.

The first function

I think the trust function of a bank is probably the most essential of its functions. We can think of banks as an intermediary
between entrepreneurs/companies and workers. There's a reason "credit" means belief or trust in latin.
Entrepreneurs and firms offer future goods and services based on predictions
and specialized knowledge. In return for these future goods and services, they buy workers using wages. However, workers
will refuse these futures goods and services, since they are not secure enough and not transferrable (this is partly related
to the third function). For example, take the car manufacturing firm Tesla. Tesla promises to provide a constant
stream of cars in the future - say 40 000 cars a year. However, their workers are unwilling to be paid in these
future promises of cars. What instead happens is that a bank takes these promises of future cars from Tesla, and
gives bank deposits in return. These bank deposits will be accepted as payment by the workers. In other words, banks
operate as an intermediatery between the firms/entrepeneurs and the workers.

Banks take the promise of future goods and services from the firms and give them back deposits. So they simulatenously
lend to the firm (as they now possess a claim on these firms future goods and services) and borrow from
the firm (they have given the firm deposits). The firm then takes these deposits and uses them
to pay the workers. You can think of bank deposits as a "universal voucher" not just for a specific firm goods and services, but for all
firm's goods and service in that country (or firms which the bank lends to).

The second function

This is the most contraversial function of banking. The promises for goods and services which the bank takes
from firms are promises for future goods and services. The bank deposits are promises for current goods
and services. This leads to the problem that if everyone withrew their deposits at once, then even a bank
which has made wise and profitable loans will go bankrupt, since it can't at one time fund all of its investors
at once.

However, there is also a benefit to this - there is a utility in having liquid funds that can be accessed at
any time. It also makes the deposits easier to transfer - an instant loan of $100 is always worth $100 (ignoring default
risk) whilst a loan of $100 receivable in a year is worth less than $100, but by how much? Having deposits
be instantly callable makes their valuation very simple.

The third function

Banks can be used as payment providers - I can transfer my money easily and quickly using my bank. However,
many companies which aren't banks provide payment solutions (e.g. Stripe, paypal, cryptocurrencies). So truth
be told, it seems plausible that this function isn't a necessary part of banking. However, this function definitely
interacts with the other two in interesting ways. For example, having maturity transformed deposits makes it simpler
to transfer them. Having deposits function as universal vouchers for goods and services adds to their transferability.

However, in modern banking, bank deposits are never truly transferred. For example, say I had a bank deposit with
Lloyds bank (a UK bank) and wanted to send $100 to my friend whos has a Santander (a Spanish bank) account. If this transfer
went through then my friend would have $100 extra I.O.Us from Santander and I would have $100 less I.O.Us from Lloyds. However,
an I.O.U of $100 from Santander is different to an I.O.U of $100 from Lloyds. If this had been a true transfer, then
I would have $100 less I.O.Us from Lloyds, and my friend would have the same number of I.O.Us from Santander and
a $100 I.O.U from Lloyds.

What happens in the modern banking system is that when I transfer $100 dollars to my friend, 3 things happen:

1. Lloyds gives a $100 I.O.U to Santander (Lloyds borrows $100 from Santander)
2. Lloyds removes a $100 I.O.U from me (Lloyds lend me $100)
3. Santander gives a $100 I.O.U to my friend (Santander borrows $100 from my friend)
4. Santander receives a $100 I.O.U from Lloyds (Santander lends $100 to Lloyds)

(Really, 1. and 4. are the same as X borrowing Y is the same as Y lending to X, but having them duplicated illustrates the point)

Now in practice, Lloyds and Santander will process so many transfers that they're lending to each other
will balance out. However, note that this is different to a cash transfer or a bond transfer, where
the issuer remains the same. E.g. if I sell you a stock or a share on an exchange, that is a transfer
of an asset.

So with these three functions, we can define a bank as an entity which issues transferable, short-term debt and
holds long-term debts.