One centimetre is exactly 10 millimetres. It is the smallest step in the metric system that people actually convert between, and despite being a simple factor of ten it is the one that slips most often, because both units appear on the same ruler.
About the units
Both units are the metre with a prefix: centi means a hundredth, milli means a thousandth. On a standard ruler the numbered divisions are centimetres and the small unnumbered ticks between them are millimetres, ten to each centimetre. That shared physical presence is what makes the pair intuitive to use and easy to misread — a measurement of "four and a half" can mean 4.5 cm or 45 mm depending on which set of marks the reader was counting, and both are the same length, but a reader who writes down 4.5 mm has lost a factor of ten.
The exact factor
The factor is exactly 10, a single decimal place. 3.7 cm is 37 mm; 12 mm is 1.2 cm; 0.8 cm is 8 mm. Because the shift is only one place, an error here is smaller than the other metric slips but harder to spot — a component specified at 25 mm and made at 2.5 cm is right, while one made at 25 cm is obviously wrong at a glance. The dangerous case is the opposite direction, where a plausible-looking number turns out to be a tenth of what was intended.
Where you meet this conversion
Jewellery and watchmaking work in millimetres, so a bracelet described as 18 cm is 180 mm of strap. Stationery and craft materials switch between the two freely: paper thickness in millimetres, sheet size in centimetres. Bolt and screw sizes are always in millimetres, while the packaging often lists lengths in centimetres. Medical imaging reports use millimetres for lesion and structure sizes precisely because the extra digit avoids ambiguity.