Repo market - the backbone of the financial system

What is the repo market? And why it's the backbone of the financial system?

The repo market is the heart of the financial system. It is the market where cash that financial institutions have and Treasury securities meet.
Large financial institutions, such as banks and brokers / dealers can fund their operations in multiple ways. They can borrow from other banks or issue debt. Or they can choose a cheaper option which is the repo market. Repo or repurchase agreement is an agreement to sell securities to buy them later at a higher price.
You can think of a repo as a short-term collateralized loan.
Dealers (or banks) have a huge amount of Treasury bonds on their balance sheet which they lend to institutions with lots of cash. After a short period of time, dealers purchase their securities at a higher price from their counterparties. The difference between the sale and repurchase price is the repo rate. Both parties benefit from the repo market.
Broker-dealers need funding, thus they lend securities that otherwise sit idle on their balance sheet. They fund themselves in a cheaper way. Institutions with lots of cash take those securities as collateral. They provide liquidity to dealers and earn interest without much risk because their collateral is usually Treasury bills. Repo market is the main source for dealers to fund themselves.
Repos tend to trade at a few basis points lower than Fed funds rate because, as already discussed, Treasury bills are pledged as collateral. In a normal funding environment, repo rate trade close Fed Funds rate. But sometimes things can and do change, reflecting the real supply / demand dynamics of the market. During hard times, demand for high quality securities increases. Since institutions only want to hold only highly rated assets, such as Treasury bills, during crises, funding rates tend to fall.
Institutions with extra liquidity can give up some yield and lend their cash at a lower rate to broker-dealers. On the contrary, the rate will increase when broker-dealers have lots of securities on their balance sheet. This is because dealers will have to pay a higher rate to borrow cash to fund themselves.