One square kilometre is exactly 1,000,000 square metres. The million is the thousand of the linear conversion squared, and it is the single most common place where a factor of a thousand is used where a million belongs.
About the units
Both units are metric and both are derived from the metre, so there is no historical complication here at all — only arithmetic. A square kilometre is the area of a square one kilometre on a side. Since a kilometre is 1,000 metres, that square measures 1,000 m by 1,000 m, and its area is 1,000 × 1,000 = 1,000,000 m². The square kilometre is the standard unit for geographic areas: countries, lakes, forests, urban footprints and weather systems. The square metre serves everything at building scale and below.
The exact factor
The factor is exactly 1,000,000, which is 10⁶. The error to guard against is using 1,000, and it is common enough to be worth naming: a lake reported as 3 km² is 3,000,000 m², not 3,000 m². The second figure would be a large garden. The intermediate unit that catches this is the hectare: 1 km² is 100 hectares and 1 hectare is 10,000 m², and multiplying those two gives the million directly. Working through hectares is a good habit precisely because the error becomes visible at the halfway point.
Where you meet this conversion
Any calculation that moves between geographic and building scale. Solar farm output is computed per square metre of panel and reported per square kilometre of site. Rainfall in millimetres over a catchment in square kilometres gives volume in cubic metres, and that calculation only works if the areal factor is right. Population density, land use planning, and habitat loss statistics all report in square kilometres while the underlying measurements are in square metres.