What does it mean when in certain publications they write population density (1000 people/km2)? Does it mean that they calculate the population density by dividing the number of people by the area of land in square meter and then they divide the result by 1000?
Population density is simply calculated by:
Number of People / Land Area
Therefore, 1000 people/km2 is the population density in your case.
Often, population density is measured in km^2 or mi^2 as finer measurements such as people/m^2 or ft^2 would not be very useful in interpretation.
According to the US Census Bureau:
Population density allows for broad comparison of settlement intensity across geographic areas. In the U.S., population density is typically expressed as the number of people per square mile of land area. The U.S. value is calculated by dividing the total U.S. population (316 million in 2013) by the total U.S. land area (3.5 million square miles).
When comparing population density values for different geographic areas, then, it is helpful to keep in mind that the values are most useful for small areas, such as neighborhoods. For larger areas (especially at the state or country scale), overall population density values are less likely to provide a meaningful measure of the density levels at which people actually live, but can be useful for comparing settlement intensity across geographies of similar scale.
They calculate the population density by dividing the number of people by the area of land in square kilometer. If you want to get in
people/m2, then you have to divide the result by
1.000 people / km2 = 0.001 people / m2 (statistically)
1.000.000 people / km2 = 1 people / m2 (statistically true. it doesn't mean that one people lives in each 1 m2)