What is wrong with a 328i BMW when a half full jug shows on the dash?

Depends on what the jug looks like and color, orange usually indicates washer fluids or non-essentials, red usually indicates danger. Check your washer, coolant overflow, brake fluid and other obvious "jugs" under the hood. Your owners manual should clearly indicate its purpose. Sensor can fail, if you correctly identify what bottle it is, its up to the "full" line by sight or stick and the lamp is lit, give the bottle a tap and see if it goes out...