It stops the programmed wash/wipe sequence on the front/rear windscreens (the press the button once to get a spray and 3 swipes of the wipers) and also stops the headlamp wash/wipe.
It supposedly does it to save the remaining fluid for necessary uses only - eg the front screen - but will only spray it whilst you've got your finger on the button.
Some people disable the screen wash warning (in the case of a bad sensor that always says that the screen wash is low, even when it's not, by unplugging the sensor, so it could be that - or your sensor could have failed in the 'always full' state, so you never get the warning.
Sensor part number is: AMR3270 if you need to replace it