One newton is 0.1019716213 kilograms-force, because one kilogram-force is exactly 9.80665 newtons. The kilogram-force is a metric unit that measures force but is named after a mass, which is precisely the confusion SI was built to eliminate.
About the units
The kilogram-force, also called the kilopond and written kgf or kp, is the gravitational force on one kilogram at standard gravity. It belongs to the older metric gravitational system, which used the kilogram-force alongside the metre and the second and was standard in continental European engineering well into the twentieth century. SI replaced it with the newton, which is defined from mass and acceleration rather than from an assumed gravitational field. The kilogram-force is now deprecated but far from extinct — it survives in older machinery, in some Asian markets and in colloquial use where people say a spring pulls with so many kilos.
The exact factor
The value is exactly 9.80665 N per kgf, since standard gravity was fixed at that figure by the third General Conference on Weights and Measures in 1901. It is a defined constant rather than a measurement: actual gravity varies from about 9.78 at the equator to 9.83 at the poles, so a kilogram-force is not quite the same real force in Stockholm as in Singapore. That variation is around half a per cent, which is negligible for a bathroom scale and not negligible in precision force measurement.
Where you meet this conversion
Older European technical documentation, particularly German, Italian and Nordic machinery manuals from before the 1980s. Spring specifications, clamping forces and cable ratings in legacy equipment are given in kilopond. Bicycle and gym equipment sometimes quotes resistance in kilograms, meaning kilograms-force. In Japan and South Korea the unit persists in some industrial contexts. Anyone commissioning or repairing older machinery meets it, and treating a kilopond figure as newtons understates the force nearly tenfold.