I am going to stick my neck out on parallax based on old memories and maybe someone will correct me if I am wrong.
Aside from sounding "neat" which is why the word is used in so many movies and sci-fi stories, it is real. It merely means that the appearance of two different points differs depending on the position of the viewer. This is easy. Pick a spot on the wall. Now put up the thumb of your right hand close to your eye and the thumb of your left hand farther away. With one eye closed, line the thumbs up with the spot on the wall.
Now, without moving your hands, move your head. Neither thumb is in line with the spot on the wall. That is parallax.
How does it occur in a scope sight? Here is where I have to go by memory, so bear with me and straighten me out where I goof.
A scope has an objective lens at the front. Light from an object (say a deer) enters that lens. The light is brought to a point (ever played with a "burning glass"?) then spreads out again but reversed. The deer's antlers are now at the bottom, and its left side is on the right. That image is "projected" on another lens, then a third lens or set of lenses magnifies and "erects" the image so it is right side up when you look in the scope.* If the crosshairs or dot is on the second lens, there will be no parallax. No matter how you move your head, the crosshairs or dot will always be fixed on the deer. But that is not feasible, since the lens would have to be movable and for mechanical and optical reasons that is not practical, though it has been done. (There are parallax free scopes though they are expensive.)
Normally, the crosshairs (or dot) will be somewhere in the scope where the image is "in the air", which means that they are not in the same optical plane as the picture you are looking at. And that difference is what causes parallax and results in the crosshairs seeming to move when your head moves.
*The same thing happens in the eye which does not have an erecting lens; the image on the retina is actually upside down. The brain reverses it or else we would see everything upside down, which would be a nuisance.
Jim