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Around 28:20 in the movie, after Ramius' opening speech for Red October's mission and while the crew is singing the Soviet anthem, he gives the numbers 2/5/0 to his navigator to use as a direction.

I've seen this three-numbers system used in a lot of sci-fi and I always brushed it off as technobabble, but this is the first time I've seen it in a historical fiction that aims for technical realism, so I guess these numbers do mean something. And searching with something as vague as "three numbers", "navigation", "direction" and "submarine" isn't precise enough for Google.

Am I right in assuming this three-numbers system is (or was) used in the real world? If so, does it have a specific name and what do the numbers represent?

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I believe this is just a bearing, a standard method of navigation that uses the 360 degrees of a circle, with 0 at true north, like so:

enter image description here

A bearing of "2-5-0" would be 250 degrees, which is roughly west-by-southwest. Saying the digits one-by-one ("two five zero" instead of "two-hundred-and-fifty") reduces the risk of miscommunications that could lead you off-course ("I thought you said two-hundred-and-fifteen!").

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    Like "m as in Mancy"? – Acccumulation Dec 6 '20 at 4:14
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    Yep, that's exactly the point of phonetic alphabets as well - to reduce the chance of critical information being misheard. – F1Krazy Dec 6 '20 at 10:17
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    Steer 250 would be with 0 degrees beeing north. Relative bearings would be given as red or green (red 90 would be straight off to the left, known as port). Also note that where "North" is depends on a number of factors (a magnetic compass will not necessarily point at the geographic north pole, search for "magnetic declination"). In this case though it does not matter as they use the same gyro compass to get bearings. (More fun reading "gyrocompass") – ghellquist Dec 6 '20 at 22:06
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    @davidbak: Absolute, although there's some ambiguity as to whether they're true or magnetic. – Joshua Dec 6 '20 at 22:10
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    @davidbak Here's a reference card for US Navy helm commands (I assume the HFRO Russian Navy would be similar): boatswainsmate.net/BM/helmcmds.pdf. – mpez0 Dec 7 '20 at 15:39

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