Banks in the modern economy are profit maximizing businesses. The simple explanation is that banks allow for the secure depositing of money for individuals and businesses. However, when banks receive a substantial amount of deposits, it becomes irrational to simply let the money sit there. As a result, banks then invest this money and have it earn interest for the bank and the depositor. From this, banks became central actors in the modern economic system.
Using a very simple model, when banks collect deposits, they seek to make this money “work” for them through investing it by lending it out to others. Since it is unlikely that depositors will demand their money all back at once, the bank can leverage its deposit collection to back larger and larger risks. In other words, they will use their deposit money to leverage larger loans and investments, thus keeping only a fraction of their deposits actually on hand. This is called “fractional reserve” banking.
The main area of significance for banks in modern financial systems are as mediators of risk. Banks are for-profit organizations that seek to use depositors funds as backing for long term investment. The brief formula is that banks collect deposits from individuals, these deposits are used as collateral for raising funds on money markets, and these funds are then put into long term investments.
Banks lend a portion of depositors' money to businesses that the bank believes will make money, hence making money for their depositors. There is no good reason for deposit money to merely collect dust in vaults, so it is lent out to those who the bank have approved in advance as a good credit risk. This means that banks oversee investments, using depositors' money as backing. Since bank loans are the main source of funding for businesses, banks actually have a massive role in overseeing investments globally.
The main effect of the significance of banks is that they have a hand in nearly all investments made in the modern economy. When one takes out a mortgage to buy a house, the bank has determined that the borrower is a good credit risk and is likely to pay the money back, including the interest which is the bank's “cut,” for taking the risk in the first place. The major concept is that since most capital is raised through banks, banks then control most investments.
When banks lend money to investors, this loan means several things: a) that the bank actually owns the enterprise (house, business, car, etc.) until the money is paid off; and b) these investments are all mediated by the bank, which means that banks measure and approve (or reject) the risks investors take. If too many investments fail, the bank fails, and the depositors' money goes to the entity that takes over the failing or failed bank. Since the 1930s, however, deposits are backed by the federal government, guaranteeing individual deposits up to $250,000 up until 2014, when the covered maximum per account goes back to $100,000.