Several meanings, but the usual one in military terms is the direction from one thing to another. I know that's a bit vague, but there are several versions ......
The direction from one point to another relative to the North used by that map. If using an Ordnance Survey map of the UK, this is the Universal Transverse Mercator (UTM) projection.
The direction of an object or feature measured relative to the magnetic pole by use of a compass. This can be converted to a Map Bearing by addition/subtraction of the appropriate Grid Magnetic Angle for that map sheet and region.
If someone is said to have "a military bearing" it means that they carry themselves in a manner generally considered exemplary among members of HM Armed Forces1. It does not mean they're carrying around a roller bearing from a Chieftain gearbox.
1Excluding the RAF... Obviously!