One knot is exactly 1.852 kilometres per hour, because a knot is one nautical mile per hour and a nautical mile is exactly 1,852 metres. Both figures are definitional, so the conversion is exact.
About the units
The knot takes its name from the method used to measure it. A log line with knots tied at regular intervals was thrown overboard and paid out for a measured time — usually 28 seconds, timed with a sandglass — and the number of knots that ran out gave the speed directly. The spacing was chosen so that one knot passing per interval equalled one nautical mile per hour. The nautical mile itself is one minute of latitude, standardised at 1,852 metres in 1929, which is what makes the whole system useful: a navigator can read distance off a chart's latitude scale and convert to time with no arithmetic beyond division.
The exact factor
The factor is exactly 1.852. In metres per second a knot is 0.514444, so a rough approximation is that knots are half of metres per second doubled — or more usefully, that 20 knots is about 37 km/h and 10 m/s is about 19.4 knots. The relationship worth having for navigation is that at 6 knots a vessel covers one nautical mile in ten minutes, which makes mental estimation of arrival times trivial and is why 6 knots is such a commonly quoted cruising speed for sailing yachts.
Where you meet this conversion
Marine and air navigation universally, including in fully metric countries, because the link between the nautical mile and latitude is too useful to abandon. Wind speed at sea and in aviation forecasts is given in knots. Ships' speeds, ocean currents and tidal streams all use it. Recreational boating instruments read in knots while the road speed of the trailer towing the boat is in kilometres per hour, which is where most people meet the conversion.