Most of the activity in the so-called overnight market in fact occurs in the morning immediately after the start of business for the day.
On the other hand, if the analyst projects that the institution will have surplus money on hand beyond that needed by its clients that day, then it will lend money on the overnight market that day.
In this context, the term "overnight" means that the cash borrowed is repaid the following day.
If, however, over the course of the day, the actual amount of money required by the institution's clients departs from that projected in the morning, it may become necessary for the institution to borrow money on the overnight market to meet this unexpected demand from its clients; conversely, if the institution finds itself with more funds on hand than it anticipated late in the day, it will then lend those funds on the overnight market.
Banks are the largest participant in the overnight market, although some other large financial institutions, e.g. mutual funds, also buy and sell on the overnight market as a way to manage unanticipated cash needs or as a temporary haven for money until the institution can decide on where to invest that money.