How does the target indicator on a jet fighter work?
There are two main questions here, mainly how does a fighter jet track a flying target, and questions about the symbols used on the Heads Up Display.
How does a fighter jet track targets
A fighter jet tracks its target(s) using its radar, which (as you are all aware) works by emitting EM waves and detecting the reflected waves bounded off by the target. The onboard computer processes this data and translates it to target information.
There are two modes of radar operation*. The first is a scan mode: the radar makes a sweep across a wide angle to look for targets. In this mode, the radar scope is wide, but target update rate is slow, and target information is coarse. The second is targeted mode: the radar focuses a narrow beam of energy at the target, which provides accurate readings with a high update rate. On the HUD, you can see &quot;200Vc&quot;, meaning the jet is closing in on the target at a relative speed of 200 knots. Below that is &quot;1000 FT&quot;, the distance to target.
* There are many modes actually, but to keep it simple, let's just focus on two.
A fighter jet does not identify a target optically nor using infrared. Neither of these two methods can provide accurate position information of the target. This may change in the future, but it is what the technology is now.
About the HUD
The HUD is from a F-18 (I am not sure which variant). Let's go over the symbols top to bottom and left to right:
Left column

On the upper left is a black square. It indicates that the trigger is pressed at this moment. It is displayed only on the recorded tape and is not visible to the pilot.
the boxed number is the indicated airspeed. It is reading 179 knots.
Going down is the angle of attack, or &quot;alpha&quot;. It is reading 20.3 degrees.
Mach speed is 0.36.
G-loading is 1.7.
The max g-loading on this flight is 7.6 G.
Below that is the time in UTC.

Center column

On the upper center, the arrow pointing upwards &quot;^&quot; is the needle of the heading indicator. Above it is the ruler marked with heading numbers, which is apparently cropped off in this image.
The cross sign below &quot;+&quot; is gun cross. The cross is always displayed at the gun inclination angle as a backup.
The &quot;w&quot; sign is the attitude indicator. In the background we can see the numbers: the aircraft is pitched 26 degrees down and banked approximately 70 degrees to the right.
&quot;GUN&quot; indicates machine gun is the selected weapon. The cross indicate it cannot be fired, most likely because this is a practice mission and master-arm is not on.
&quot;0&quot; is the number of bullets left.
Near the bottom edge of the image, a bit to the right of center line, is the flight path indicator, a circle with three bars extending from its left, top and right respectively. It shows where the aircraft is travelling to, and it is useful for landing or flying low near terrain.

Right column

Current altitude is 15180 feet MSL.
Target closure rate is 200 knots.
Range to target is 1000 feet. If the range is longer than 1 nautical miles, it will display in nautical miles instead, up to the nearest 0.1 nautical mile (e.g. 2.3)

Symbol around the target

This particular circle is the target reticle for gun mode. A bigger circle is displayed if it is in missiles mode.
The center dot shows where the bullet will hit if the gun is pressed at this very moment. The circle moves around the HUD as the jet is maneuvered. For example, if the pilot pulls on the stick, the circle will move towards the bottom of the HUD because that is where the bullets are going.
Targets are identified by a square box on the HUD. The square is not displayed when the gun reticle overlaps with the target, which is the scenario in this image.
&quot;IN LAR&quot; means In Launch Acceptability Region. &quot;IN LAR&quot; is displayed instead of &quot;SHOOT&quot; because the target is designated as friendly. If the target is designated as hostile, &quot;SHOOT&quot; will be displayed instead.
Below the letters &quot;LA&quot;, we can see a bold portion from 12'o clock to 1'o clock on the circle, and a mark at 1'o clock. This is the range to target. The mark rotates clockwise as target distance increases. For example, if the bold portion is instead from 12'o clock to 3'o clock, the target range will be 3000 feet.
There is a similar mark on the circle slightly pass 6'o clock, but the mark is outside the circle. This is the maximum range of the currently selected weapon. By comparing the bold portion of the circle to this mark, a pilot can tell whether the target is within range of the current weapon.
I have no idea what the &quot;x&quot; means.