There are 1,000 grams in a kilogram.
Each gram of water has a volume of 1 milliliter (the question said millimeter but that measures length and I think it was meant to say milliliter).
Since there are 1,000 grams with a volume of 1 millimeter each, the volume is 1,000 milliliters, which is equal to 1 liter.
Hope this helps!