First, definitions. The overnight rate is the interest rate, called the effective Federal Funds rate, that is used when banks lend money to each other in the Federal Funds Market to meet bank reserve requirements. These loans do not have any collateral.
The repo rate is the interest rate, called the repurchase agreements rate, (and the opposite - reverse repo rate) used when the FOMC (Federal Open Market Committee) wants to adjust the country's money supply by way of adjusting the level of credit.
When FOMC wants to increase credit during a recession, the FOMC will loan funds to specific Treasury Dealers, who in turn, will provide treasuries as collateral. These funds are deposited (credited) to the dealers' banks, which will cause funds to be available for loans to the general public. The dealers will pay the loans within a few days, with interest (repo rate).
If, as an example, the economy is showing inflation, then FOMC wants to decrease credit. The opposite occurs. The FOMC becomes the borrower, receiving loans from and issuing treasuries to Treasury Dealers as collateral. Again, the loans are usually paid within a short period of time, and the reverse repo rate is used.
Both the repo and reverse repo rates are part of the Repo Market.
Now, here's the connection between the two markets, Federal Funds and Repo, in the monetary policy arena.
In the news, the public hears about an interest rate change by the Fed (FOMC). This is the "targeted" Federal Funds rate. The FOMC springs into action during business hours, with the Treasury Dealers in the Repo market, adjusting the country's credit, using the targeted Federal Funds rate as a benchmark for the repo (reverse repo) rate.
During evening hours, the banks are loaning to each other in the Federal Funds Market, using the repo rate as a benchmark for the effective Federal Funds rate. The effective rate (no collateral) will be slightly higher than the repo rate (has collateral).
The next day, the FOMC will review results from the previous day to see how well the effective rate met the targeted rate, and the Repo Rate "dance" starts all over again. That evening, the banks will do a repeat performance of the Federal Funds "dance".