where does this hose connect?

as they say - a picture is worth 1000 words....I found the OP's picture & posted it below.

If you're talking about that EXTRA hose (against the wall ?) with the open end - it is used to WINTERIZE your water system.

stick that hose in a gallon (or more) of RV water/line antifreeze (pink stuff available at walmart) and throw the valve on top of the pump)....

turn the water on, and the pump will suck the winterizing antifreeze thru your system to evaluate water from the lines & replace it with antifreeze (to keep water lines from freezing & busting).

if you're talking about the RIBBED hose (further to the left) that (looks like) it goes into the floor - thats is very likely your water tank FILL hose.

I'll take a stab at it: maybe the uptake hose for winterizing. Used to stick into a jug of RV anti-freeze and then pump through the system.
??

No picture