Why is water standing in my passenger rear floor board?

There are a few possibilities;
Since it is not related to rain pouring at the time, rear window gaskets are out.
However the front fresh air box is often a problem especially in cars that are not garaged. The intake grid in front of the windhsield lets in, "Fresh Air" when you turn the climate control off of re-circulate. There is a cowl system that usually uses several layers to prevent water from passing through the air intake which is on the passenger side above the A/C evaporator. When it starts the fluid can collect in the evaportor box which is to the right of the heater core box and coe out when forward motion begins and end up in the rear footwell. When this happens, you should still feel the carpet wet in the front. Ther reasons the leak happens can be from years of dirt and small debris clogging the drain or, "weep" joles at wither end of the box that exit near the top of the front tire and run down inside the feder well cover out to the ground. Also, seals can go bad as well as the plugs that hold the multi-layered diverter in place. I had one leak that had a plug that would not hold a seal and it was at the box wall itself which is the last line of defense against leaks. It leaked right past the retaining plug. Some boxes can have the cowl covers removed from the outside while others require somw under dash work.

The other possibility is that the heater core is leaking. You will generally smeall this but it can happen in the same fashion as the cowl box. A heater core is a small radiator that produces heat for the interior and can leak if it gets a hole in it and produce the same affects.

So, check the front carpet for it being damp as well as if it is water or anti-freeze and that should give you the clues to stopp the leak.