One millimetre is 2.8346456693 points, because a point is exactly 1/72 of an inch and an inch is exactly 25.4 mm. The awkward decimal is the price of a typographic system built on inches inside a metric world.
About the units
The PostScript point, also called the desktop publishing point, is exactly 1/72 inch — 0.352777... mm. That definition dates only from the 1980s. Before it, typography used points that were not quite the same: the American Johnson pica point was 1/72.27 inch, which survives as the TeX point and differs by about a third of a per cent; the French Didot point was 0.376 mm, noticeably larger and used across continental Europe well into the twentieth century. A document set in Didot points and reproduced with PostScript points comes out six per cent small.
The exact factor
The exact value is 25.4 ÷ 72 = 0.3527777... mm per point, so 1 mm is 2.83464566929134 points. Useful equivalents: 10 pt is 3.53 mm, and a 5 mm margin is 14.17 pt. Because neither number is round, layout software works internally in one unit and displays the other, and rounding differences of a hundredth of a millimetre appear when a document moves between programs. Those differences are invisible on paper and can shift a text frame by a pixel on screen.
Where you meet this conversion
Print production, where page dimensions and margins are metric in Europe but type sizes and leading are in points everywhere. A European book designer specifies a 128 × 198 mm trim size with 10.5 pt type on 14 pt leading, mixing the systems in a single specification. Bleed, trim and safety margins are in millimetres while rules, borders and type are in points. Preflight checks and imposition software convert constantly, which is why a PDF's internal coordinate system is in points regardless of what the designer typed.