One megahertz is exactly 1,000 kilohertz. This is the radio pair: the boundary between the long and medium wave bands below and the FM and television bands above runs straight through it.
About the units
Both units are the hertz with an SI prefix. The range they cover is where broadcast radio lives, and the frequency determines how the signal propagates. Long wave, below 300 kHz, follows the curvature of the Earth and carries hundreds of kilometres. Medium wave, 530 to 1,700 kHz, does the same at night when the ionosphere reflects it. Short wave, 3 to 30 MHz, bounces off the ionosphere and crosses continents. FM broadcasting sits at 87.5 to 108 MHz and is limited to line of sight. Each of those behaviours follows from the wavelength, which is the speed of light divided by the frequency.
The exact factor
The factor is exactly 1,000. The wavelength relationship is what makes the numbers meaningful: at 1 MHz the wavelength is 300 metres, at 100 MHz it is 3 metres, and at 1 kHz it would be 300 kilometres. That is why long wave transmitter masts are enormous and FM antennas fit on a car roof — an efficient antenna is a substantial fraction of a wavelength. Radio dials are marked in kilohertz for AM and megahertz for FM precisely because the two bands sit either side of this conversion.
Where you meet this conversion
Radio in every form. Amateur radio allocations, aviation communication at 118 to 137 MHz, marine VHF at 156 to 174 MHz, and broadcast bands are all specified across this range. Older computer clock speeds were in megahertz, and the frequencies of crystal oscillators, intermediate frequency stages and switching converters all fall here. Medical ultrasound transducers are specified in megahertz, where higher frequency gives better resolution but less penetration.