Very simply, parallax is an apparent motion of an object due to a change in observation position. Let me start with an example. Here are two photos. I took a picture of the cabinet in the background from two slightly different positions. In the foreground is a clone trooper that did not actually move.
I added the dotted line so you could see how the clone trooper appeared to change positions with respect to the background. Here is a diagram of the camera in the two positions along with the toy.
Since the camera changed positions, the object that is closer appears to have moved with respect to the objects that are farther away. You don’t need a clone trooper toy to see an example of parallax. You can do this with your thumb. Hold your thumb out in front of your face at arms length. Close one eye and line your thumb up with some object in the distance. Then switch eyes that you are looking out of. Here is a diagram.
If you can’t tell from my drawing, this is a diagram looking down on a person.
So, how is this useful? Well, early astronomers like the Greeks knew about parallax. If you know the distance between the two viewing locations and if you measure the apparent change in position of the object you can calculate the distance of the object. Great, the Greeks could use this to show that the Earth is orbiting the Sun (rather than the other way around). If you look at a star now and then 6 months later, you have changed your observation location by twice the radius of the Earth’s orbit. The closer stars should move relative to the stars that are more distant.
When the Greeks looked for the parallax in stars, they measured none. This must mean that the Earth is not orbit the Sun. However, the closest star only changes its apparent position by about 1 arcsecond (that is like 0.0003 degrees). A very very difficult angle to detect and measure. So, when Aristarcus proposed that the Sun is so big that the Earth must orbit it, all the other Greeks made fun of him and called him names.