Excellent answer!!!
If the Fed funds rate is only used for overnight borrowing, why is it such a big deal when Powell & Co. moves it?
Because it serves as a benchmark for basically every short-term interest rate product, such as LIBOR, Eurodollars, and the bank Prime rate. There is an "overnight rate" but also a "benchmark rate" which go hand in hand but are only indirectly related. The Fed actually doesn't "lower" the benchmark rate - it buys short-term T-bills/Bonds until the rate approximates the target. If it wants to "raise" the rate, it sells T-Bills/Bonds until the rate hits a target window.
As the theory goes (which isn't really working very well in Europe or Japan), Fed cuts benchmark, which widens bank profit margins. Banks then lend more because they have more margin to work with, which injects capital into the economy. More capital -> more factories/data farms/projects -> more jobs/better economy. Because more banks are lending, it generates competition, which lowers longer-term rates such as mortgages, which reduce effective housing costs.
Lowering rates also creates a "cash is trash" phenomenon, because money market funds and deposit accounts will not return enough to keep up with inflation, forcing people to invest in riskier asset classes like stocks and corp bonds.
This is all THEORY, of course, and, at the lower bounds, it amounts to "pushing on a rope" if there are other factors in play. (And there will always be other factors in play!) There is the obvious risk of too much activity from low rates leading to inflation.
P.S. I probably got the terms for the two different fed funds rates wrong, but the general idea is correct.