2D shooter plataform aim,tutorial please?

As you'll know, Unity uses 3D coordinates, however the screen (the thing the camera displays) is 2D, as well as your mouse-coordinates.

The first 2 Lines in the Update

 mouse_pos = Input.mousePosition;
 mouse_pos.z = -20;

obtain the position of the mouse cursor on the screen and actually moves the position 20 "in front" of the screen. Next, the targeted objects position is obtained and transformed into screen-space:

 object_pos = Camera.main.WorldToScreenPoint(target.position);

What this does, is that it takes the position of the object target in the game engine (the usual x/y/z coordinate) and transforms it to the coordinate system of the screen. So if you see an object ingame, and it's, let's say, 100 pixels from the bottom and from the left on your screen, this operation actually gives you that: a Vector3 that says it's (100,100,Z).

Now here comes the weird part with the Z-coordinate. As we can read in the WorldToScreenPoint-Documentation, "the z position is in world units from the camera". I assume the guy who wrote this script had his camera 20 units away from his objects, that's why he sets the mouse_pos.z to -20 above. Personally I'd just set all the Z positions to 0, to get 2D-Coordinates no matter where the camera is.

 mouse_pos.x = mouse_pos.x - object_pos.x;
 mouse_pos.y = mouse_pos.y - object_pos.y;
 angle = Mathf.Atan2(mouse_pos.y, mouse_pos.x) * Mathf.Rad2Deg;

This part is simple, straight forward math. ;) He takes the X and Y distance of the mouse and the object on the screen, and calculates the angle. Just imagine a right angle triangle with the catheti beeing the x and y distance. In case you don't know trigonometry well, just know that tan(angle) = delta_y/delta_x, and therefore the angle = atan(y/x), which is exactly what MathF.Atan2(y,x) does. :)

 transform.rotation = Quaternion.Euler(Vector3(0, 0, angle));

Quaternions represent a rotation. Quaternion.Euler returns the rotation around the X/Y/Z axis defined by a Vector3. If the Vector3 is (0,0,45), that means it'll be rotated by 45° around the z axis. Therefore this line rotates the object to look towards the target-object, since that's what "angle" represents.

I'm not exactly sure what the Aim-Line at the bottom is supposed to be, since it does nothing except transform.rotation = Quaternion.FromToRotation(Vector3.up*5, Vector3.zero). When is that thing called?

What I'm presonally missing in this script, is a section where he checks wether the mouse cursor is to the left or to the right of the object, since you'll have to mirror the gun if the mouse cursor is to the left, or it'll stand on its head. :)