Simple and practical (popular) answer:
1 liter of water "weighs" 1 kg.
In depth answer:
1 liter of water is rarely iqual to 1 kg.
To understand why, we should remember the concept os density.
Density is the ratio of mass of a body divided by its volume., or
Density is the mass per unit volume of a substance.
Density = Mass / Volume or
Mass = Density x Volume
There are issues in the simple answer above:
1 - Kg measures mass not weight, it actually measures mass. But, On Earth, people assumes mass is the same as weight, if that makes it easier (but it is not strictly correct).
2 - The density of water varies with temperature and pressure. (see table below)
That is why we said above that 1 liter of water is rarely equal to 1 kg. When temperature and/or pressure fluctuates, 1 liter of water can contain more or less water molecules (more or less mass). The density varies as mass varies because 'Density = Mass/Volume'.
Why exactly 1?
Water was set as the standard because water is the most important of all liquids and the most abundant substance on the earth. So, it was logical to let 1 kg be the weight of 1l of water.
Table: density and weight (mass) of water, at standard sea-level atmospheric pressure