One millisecond is exactly 0.001 seconds — a thousandth. It is the timescale of human perception and of computer networking, which is why it is the unit almost every latency figure is quoted in.
About the units
The millisecond is the second with the SI prefix milli. Its significance is that it sits at the boundary of what a person can notice. Human visual reaction time is around 200 to 250 milliseconds, and a delay under about 100 ms in an interface feels instantaneous while one over 300 ms feels sluggish. Below the millisecond the microsecond and nanosecond take over, and those are the timescales of processor cycles and of light propagation — light travels about 30 centimetres in a nanosecond, which is the physical limit that constrains how fast a signal can cross a circuit board.
The exact factor
The factor is exactly 1,000. The relationships that matter in practice are to frequency and distance. A frame rate of 60 per second means 16.7 ms per frame, and 120 per second means 8.3 — the numbers behind display refresh rates. A network round trip of 20 ms means a signal travelled roughly 4,000 kilometres in fibre, since light moves at about two thirds of its vacuum speed in glass, which is why intercontinental latency has a hard floor no amount of engineering can lower.
Where you meet this conversion
Network latency, audio and video synchronisation, and interface responsiveness. Audio processing measures buffer sizes in milliseconds, and a musician playing through a digital system notices delay above about 10 ms. Photography uses fractions of a second for shutter speed, where 1/500 is 2 ms. In medicine, the intervals on an ECG are measured in milliseconds and the diagnostic thresholds are tight — a QRS complex over 120 ms indicates a conduction problem.