The terminology differs a bit with special effects. I'd call them an "oriented billboard" or a "ribbon".

You've got a start point A and an end point B for the beam, and you want to draw a quad from A to B. The problem is the orientation of the quad. If, say you choose your 4 points of the quad to be slightly to the left & right of A & B, then when viewed from perfectly side-on, the quad won't be visible. When viewed from side on, you want to choose your 4 points to be slightly above & below of A & B...

So, you need to procedurally calculate some offset, which you can add to A & B to expand this line into a quad, so that it look good from every view angle. We want our offset to be tangental to the direction of the line (*i.e. the direction "normalize(B-A)" should be pointing 90º from our offset direction*), but also tangential to the direction that the camera is looking.

You'd want to be comfortable with the basics of linear algebra to make these kinds of effects, some specific tools you'd use are the dot product and cross product.

If you calculate the cross product of the direction of the laser and the direction of the view (and normalize the result), this will produce the tangential direction that you're looking for, which can be used as an offset to expand your line into a quad.