Parallax is the apparent movement of the reticle across the target when your eye moves behind the scope.
The easiest way I know to explain it is the same way I teach it in a class.
Hold both thumbs up in front of your face. Hold your left thumb farther away and your right thumb closer to your face, with about a foot of separation between them. Now keep your hands completely still and move your head from side to side.
What does your right thumb appear to do?
It looks like it moves from side to side across your left thumb. But did you actually move your thumb? No.
That apparent movement is parallax.
In this example, your left thumb represents the target image and your right thumb represents the reticle. They appear to move relative to each other because they are not on the same optical plane.
Now push your thumbs together until they are touching, then move your head from side to side again. The apparent movement disappears. That is essentially what you are doing when you adjust parallax in a rifle scope. You are bringing the target image and the reticle onto the same focal plane so that moving your eye behind the optic no longer causes the reticle to appear to move across the target.
Why does that matter?
If parallax is not properly adjusted, a change in your eye position can create an aiming error even though the rifle itself has not moved.
The simple version is:
Parallax is apparent reticle movement caused by the target image and reticle not being on the same optical plane. Adjusting parallax brings them together and removes that apparent movement.
If you want to keep learning about rifle optics, read our Shorts on What Is MOA? and What Is a MIL?, then go deeper with our full article on MOA vs. MIL.